<!DOCTYPE html>
<html lang="zh-CN">
<head>
  <meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=2">
<meta name="theme-color" content="#222">
<meta name="generator" content="Hexo 5.1.1">
  <link rel="apple-touch-icon" sizes="180x180" href="/images/apple-touch-icon-next.png">
  <link rel="icon" type="image/png" sizes="32x32" href="/images/oldimgs/32.ico">
  <link rel="icon" type="image/png" sizes="16x16" href="/images/oldimgs/16.ico">
  <link rel="mask-icon" href="/images/logo.svg" color="#222">

<link rel="stylesheet" href="/css/main.css">

<link rel="stylesheet" href="//fonts.googleapis.com/css?family=sans-serif:300,300italic,400,400italic,700,700italic|Ubuntu:300,300italic,400,400italic,700,700italic|Roboto:300,300italic,400,400italic,700,700italic|'Open+Sans':300,300italic,400,400italic,700,700italic|'Microsoft+YaHei':300,300italic,400,400italic,700,700italic|sans-serif;:300,300italic,400,400italic,700,700italic|Source+Code+Pro:300,300italic,400,400italic,700,700italic|monospace:300,300italic,400,400italic,700,700italic&display=swap&subset=latin,latin-ext">

<link rel="stylesheet" href="//cdn.jsdelivr.net/npm/@fortawesome/fontawesome-free@5.14.0/css/all.min.css">
  <link rel="stylesheet" href="//cdn.jsdelivr.net/npm/animate.css@3.1.1/animate.min.css">
  <link rel="stylesheet" href="//cdn.jsdelivr.net/npm/pace-js@1.0.2/themes/blue/pace-theme-minimal.css">
  <script src="//cdn.jsdelivr.net/npm/pace-js@1.0.2/pace.min.js"></script>

<script class="hexo-configurations">
    var NexT = window.NexT || {};
    var CONFIG = {"hostname":"http:/ShuYuMo2003.github.io","root":"/","scheme":"Mist","version":"8.0.0","exturl":false,"sidebar":{"position":"left","width":230,"display":"post","padding":18,"offset":12},"copycode":true,"bookmark":{"enable":false,"color":"#222","save":"auto"},"fancybox":false,"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"motion":{"enable":true,"async":false,"transition":{"post_block":"fadeIn","post_header":"fadeInDown","post_body":"fadeInDown","coll_header":"fadeInLeft","sidebar":"fadeInUp"}},"prism":false,"i18n":{"placeholder":"搜索...","empty":"没有找到任何搜索结果：${query}","hits_time":"找到 ${hits} 个搜索结果（用时 ${time} 毫秒）","hits":"找到 ${hits} 个搜索结果"},"path":"search.xml","localsearch":{"enable":true,"trigger":"auto","top_n_per_article":1,"unescape":false,"preload":false}};
  </script>

  <meta name="description" content="Part 2.1 模拟 [P2482 SDOI2010]猪国杀 P3693 琪露诺的冰雪小屋 [P5380 THUPC2019]鸭棋  Part 2.2 排序算法">
<meta property="og:type" content="article">
<meta property="og:title" content="做题计划">
<meta property="og:url" content="2019/%E5%81%9A%E9%A2%98%E8%AE%A1%E5%88%92/index.html">
<meta property="og:site_name" content="Shu Yu Mo&#39;s blog">
<meta property="og:description" content="Part 2.1 模拟 [P2482 SDOI2010]猪国杀 P3693 琪露诺的冰雪小屋 [P5380 THUPC2019]鸭棋  Part 2.2 排序算法">
<meta property="og:locale" content="zh_CN">
<meta property="article:published_time" content="2019-06-24T00:06:00.000Z">
<meta property="article:modified_time" content="2020-09-05T03:46:40.164Z">
<meta property="article:author" content="舒雨墨">
<meta property="article:tag" content="Shu Yu Mo&#39;s blog">
<meta property="article:tag" content="Blog">
<meta property="article:tag" content="OI">
<meta property="article:tag" content="Dr_OldSu">
<meta property="article:tag" content="舒阳">
<meta property="article:tag" content="life">
<meta property="article:tag" content="生活">
<meta property="article:tag" content="信息竞赛">
<meta property="article:tag" content="Shu_Yu_Mo">
<meta property="article:tag" content="ShuYuMo">
<meta property="article:tag" content="东营市第一中学">
<meta name="twitter:card" content="summary">


<link rel="canonical" href="2019/做题计划/">


<script data-pjax class="page-configurations">
  // https://hexo.io/docs/variables.html
  CONFIG.page = {
    sidebar: "",
    isHome : false,
    isPost : true,
    lang   : 'zh-CN'
  };
</script>

  <title>做题计划 | Shu Yu Mo's blog</title>
  






  <noscript>
  <style>
  body { margin-top: 2rem; }

  .use-motion .menu-item,
  .use-motion .sidebar,
  .use-motion .post-block,
  .use-motion .pagination,
  .use-motion .comments,
  .use-motion .post-header,
  .use-motion .post-body,
  .use-motion .collection-header {
    visibility: visible;
  }

  .use-motion .header,
  .use-motion .site-brand-container .toggle,
  .use-motion .footer { opacity: initial; }

  .use-motion .site-title,
  .use-motion .site-subtitle,
  .use-motion .custom-logo-image {
    opacity: initial;
    top: initial;
  }

  .use-motion .logo-line {
    transform: scaleX(1);
  }

  .search-pop-overlay, .sidebar-nav { display: none; }
  .sidebar-panel { display: block; }
  </style>
</noscript>

</head>

<body itemscope itemtype="http://schema.org/WebPage" class="use-motion">
  <div class="headband"></div>

  <main class="main">
    <header class="header" itemscope itemtype="http://schema.org/WPHeader">
      <div class="header-inner"><div class="site-brand-container">
  <div class="site-nav-toggle">
    <div class="toggle" aria-label="切换导航栏">
        <span class="toggle-line"></span>
        <span class="toggle-line"></span>
        <span class="toggle-line"></span>
    </div>
  </div>

  <div class="site-meta">

    <a href="/" class="brand" rel="start">
      <i class="logo-line"></i>
      <h1 class="site-title">Shu Yu Mo's blog</h1>
      <i class="logo-line"></i>
    </a>
      <p class="site-subtitle" itemprop="description">远行者</p>
  </div>

  <div class="site-nav-right">
    <div class="toggle popup-trigger">
        <i class="fa fa-search fa-fw fa-lg"></i>
    </div>
  </div>
</div>



<nav class="site-nav">
  <ul class="main-menu menu">
        <li class="menu-item menu-item-home">

    <a href="/" rel="section"><i class="fa fa-home fa-fw"></i>首页</a>

  </li>
        <li class="menu-item menu-item-about">

    <a href="/about/" rel="section"><i class="fa fa-user fa-fw"></i>关于</a>

  </li>
        <li class="menu-item menu-item-tags">

    <a href="/tags/" rel="section"><i class="fa fa-tags fa-fw"></i>标签</a>

  </li>
        <li class="menu-item menu-item-links">

    <a href="/link/" rel="section"><i class="fa fa-th fa-fw"></i>links</a>

  </li>
        <li class="menu-item menu-item-archives">

    <a href="/archives/" rel="section"><i class="fa fa-archive fa-fw"></i>归档</a>

  </li>
        <li class="menu-item menu-item-templates">

    <a href="/port/" rel="section"><i class="fa fa-heartbeat fa-fw"></i>Templates</a>

  </li>
        <li class="menu-item menu-item-latex">

    <a href="/LaTeX-syntax.html" rel="section"><i class="fa fa-heartbeat fa-fw"></i>LaTeX</a>

  </li>
        <li class="menu-item menu-item-sitemap">

    <a href="/sitemap.xml" rel="section"><i class="fa fa-sitemap fa-fw"></i>站点地图</a>

  </li>
      <li class="menu-item menu-item-search">
        <a role="button" class="popup-trigger"><i class="fa fa-search fa-fw"></i>搜索
        </a>
      </li>
  </ul>
</nav>



  <div class="search-pop-overlay">
    <div class="popup search-popup">
        <div class="search-header">
  <span class="search-icon">
    <i class="fa fa-search"></i>
  </span>
  <div class="search-input-container">
    <input autocomplete="off" autocapitalize="off" maxlength="80"
           placeholder="搜索..." spellcheck="false"
           type="search" class="search-input">
  </div>
  <span class="popup-btn-close">
    <i class="fa fa-times-circle"></i>
  </span>
</div>
<div class="search-result-container no-result">
  <div class="search-result-icon">
    <i class="fa fa-spinner fa-pulse fa-5x"></i>
  </div>
</div>

    </div>
  </div>

</div>
        
  
  <div class="toggle sidebar-toggle">
    <span class="toggle-line"></span>
    <span class="toggle-line"></span>
    <span class="toggle-line"></span>
  </div>

  <aside class="sidebar">

    <div class="sidebar-inner sidebar-nav-active sidebar-toc-active">
      <ul class="sidebar-nav" style="display:none;">
        <li class="sidebar-nav-toc">
          文章目录
        </li>
        <li class="sidebar-nav-overview">
          站点概览
        </li>
      </ul>

      <!--noindex-->
      <section class="post-toc-wrap sidebar-panel">

        <div class="site-author animated" itemprop="author" itemscope itemtype="http://schema.org/Person">
    <img class="site-author-image" itemprop="image" alt="舒雨墨"
      src="/images/avatar.jpg">
  <p class="site-author-name" itemprop="name">舒雨墨</p>
  <div class="site-description" itemprop="description"></div>
</div>
<div class="site-state-wrap animated">
  <nav class="site-state">
      <div class="site-state-item site-state-posts">
          <a href="/archives/">
        
          <span class="site-state-item-count">106</span>
          <span class="site-state-item-name">日志</span>
        </a>
      </div>
      <div class="site-state-item site-state-categories">
        <span class="site-state-item-count">28</span>
        <span class="site-state-item-name">分类</span>
      </div>
      <div class="site-state-item site-state-tags">
            <a href="/tags/">
          
        <span class="site-state-item-count">53</span>
        <span class="site-state-item-name">标签</span></a>
      </div>
  </nav>
</div>
  <div class="links-of-author animated">
      <span class="links-of-author-item">
        <a href="https://github.com/ShuYuMo2003" title="GitHub → https:&#x2F;&#x2F;github.com&#x2F;ShuYuMo2003" rel="noopener" target="_blank"><i class="fab fa-github fa-fw"></i>GitHub</a>
      </span>
      <span class="links-of-author-item">
        <a href="https://www.luogu.com.cn/user/44615" title="Luogu → https:&#x2F;&#x2F;www.luogu.com.cn&#x2F;user&#x2F;44615" rel="noopener" target="_blank"><i class="fab fa-github fa-fw"></i>Luogu</a>
      </span>
      <span class="links-of-author-item">
        <a href="mailto:sujiayi2003@gmail.com" title="E-Mail → mailto:sujiayi2003@gmail.com" rel="noopener" target="_blank"><i class="fa fa-envelope fa-fw"></i>E-Mail</a>
      </span>
      <span class="links-of-author-item">
        <a href="https://twitter.com/JiaYiSu5" title="Twitter → https:&#x2F;&#x2F;twitter.com&#x2F;JiaYiSu5" rel="noopener" target="_blank"><i class="fab fa-twitter fa-fw"></i>Twitter</a>
      </span>
  </div>



        <hr/>
          <div class="post-toc animated"><ol class="nav"><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-2-1-%E6%A8%A1%E6%8B%9F"><span class="nav-number">1.</span> <span class="nav-text">Part 2.1 模拟</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-2-2-%E6%8E%92%E5%BA%8F%E7%AE%97%E6%B3%95"><span class="nav-number">2.</span> <span class="nav-text">Part 2.2 排序算法</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-2-3-%E4%BA%8C%E5%88%86%E7%AD%94%E6%A1%88"><span class="nav-number">3.</span> <span class="nav-text">Part 2.3 二分答案</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-2-4-%E5%88%86%E6%B2%BB"><span class="nav-number">4.</span> <span class="nav-text">Part 2.4 分治</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-2-5-%E8%B4%AA%E5%BF%83"><span class="nav-number">5.</span> <span class="nav-text">Part 2.5 贪心</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-2-6-%E9%AB%98%E7%B2%BE%E5%BA%A6"><span class="nav-number">6.</span> <span class="nav-text">Part 2.6 高精度</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Part-3-%E6%90%9C%E7%B4%A2"><span class="nav-number"></span> <span class="nav-text">Part 3 搜索</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-3-1-%E6%B7%B1%E5%BA%A6%E4%BC%98%E5%85%88%E6%90%9C%E7%B4%A2"><span class="nav-number">1.</span> <span class="nav-text">Part 3.1 深度优先搜索</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-3-2-%E5%B9%BF%E5%BA%A6%E4%BC%98%E5%85%88%E6%90%9C%E7%B4%A2"><span class="nav-number">2.</span> <span class="nav-text">Part 3.2 广度优先搜索</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-3-3-%E8%AE%B0%E5%BF%86%E5%8C%96%E6%90%9C%E7%B4%A2"><span class="nav-number">3.</span> <span class="nav-text">Part 3.3 记忆化搜索</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-3-4-%E6%90%9C%E7%B4%A2%E7%9A%84%E5%89%AA%E6%9E%9D"><span class="nav-number">4.</span> <span class="nav-text">Part 3.4 搜索的剪枝</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-3-5-%E5%8F%8C%E5%90%91%E6%90%9C%E7%B4%A2"><span class="nav-number">5.</span> <span class="nav-text">Part 3.5 双向搜索</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-3-6-A"><span class="nav-number">6.</span> <span class="nav-text">Part 3.6 A*</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-3-7-IDA"><span class="nav-number">7.</span> <span class="nav-text">Part 3.7 IDA*</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Part-4-%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92"><span class="nav-number"></span> <span class="nav-text">Part 4 动态规划</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-4-1-%E7%BA%BF%E6%80%A7%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92"><span class="nav-number">1.</span> <span class="nav-text">Part 4.1 线性动态规划</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-4-2-%E8%83%8C%E5%8C%85%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92"><span class="nav-number">2.</span> <span class="nav-text">Part 4.2 背包动态规划</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-4-3-%E5%8C%BA%E9%97%B4%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92"><span class="nav-number">3.</span> <span class="nav-text">Part 4.3 区间动态规划</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-4-4-%E6%A0%91%E5%BD%A2%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92"><span class="nav-number">4.</span> <span class="nav-text">Part 4.4 树形动态规划</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-4-5-%E7%8A%B6%E6%80%81%E5%8E%8B%E7%BC%A9%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92"><span class="nav-number">5.</span> <span class="nav-text">Part 4.5 状态压缩动态规划</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-4-6-%E5%80%8D%E5%A2%9E%E4%BC%98%E5%8C%96%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92"><span class="nav-number">6.</span> <span class="nav-text">Part 4.6 倍增优化动态规划</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-4-7-%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E4%BC%98%E5%8C%96%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92"><span class="nav-number">7.</span> <span class="nav-text">Part 4.7 数据结构优化动态规划</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-4-8-%E5%8D%95%E8%B0%83%E9%98%9F%E5%88%97%E4%BC%98%E5%8C%96%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92"><span class="nav-number">8.</span> <span class="nav-text">Part 4.8 单调队列优化动态规划</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-4-9-%E6%96%9C%E7%8E%87%E4%BC%98%E5%8C%96%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92"><span class="nav-number">9.</span> <span class="nav-text">Part 4.9 斜率优化动态规划</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-4-10-%E5%9B%9B%E8%BE%B9%E5%BD%A2%E4%B8%8D%E7%AD%89%E5%BC%8F%E4%BC%98%E5%8C%96%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92"><span class="nav-number">10.</span> <span class="nav-text">Part 4.10 四边形不等式优化动态规划</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-4-11-%E6%95%B0%E4%BD%8D%E7%BB%9F%E8%AE%A1%E7%B1%BB%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92"><span class="nav-number">11.</span> <span class="nav-text">Part 4.11 数位统计类动态规划</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-4-12-%E8%BD%AE%E5%BB%93%E7%BA%BF%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92"><span class="nav-number">12.</span> <span class="nav-text">Part 4.12 轮廓线动态规划</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Part-5-%E5%AD%97%E7%AC%A6%E4%B8%B2"><span class="nav-number"></span> <span class="nav-text">Part 5 字符串</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-5-1-%E5%AD%97%E7%AC%A6%E4%B8%B2%E5%93%88%E5%B8%8C"><span class="nav-number">1.</span> <span class="nav-text">Part 5.1 字符串哈希</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-5-2-KMP"><span class="nav-number">2.</span> <span class="nav-text">Part 5.2 KMP</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-5-3-Manacher"><span class="nav-number">3.</span> <span class="nav-text">Part 5.3 Manacher</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-5-4-Trie%E6%A0%91"><span class="nav-number">4.</span> <span class="nav-text">Part 5.4 Trie树</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-5-5-AC%E8%87%AA%E5%8A%A8%E6%9C%BA"><span class="nav-number">5.</span> <span class="nav-text">Part 5.5 AC自动机</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-5-6-%E5%90%8E%E7%BC%80%E6%95%B0%E7%BB%84"><span class="nav-number">6.</span> <span class="nav-text">Part 5.6 后缀数组</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-5-7-%E5%90%8E%E7%BC%80%E8%87%AA%E5%8A%A8%E6%9C%BA"><span class="nav-number">7.</span> <span class="nav-text">Part 5.7 后缀自动机</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Part-6-%E6%95%B0%E5%AD%A6"><span class="nav-number"></span> <span class="nav-text">Part 6 数学</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-6-1-%E6%95%B4%E9%99%A4%E7%9B%B8%E5%85%B3"><span class="nav-number">1.</span> <span class="nav-text">Part 6.1 整除相关</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-6-1-1-%E7%B4%A0%E6%95%B0"><span class="nav-number">1.1.</span> <span class="nav-text">Part 6.1.1 素数</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-6-1-2-%E6%9C%80%E5%A4%A7%E5%85%AC%E7%BA%A6%E6%95%B0"><span class="nav-number">1.2.</span> <span class="nav-text">Part 6.1.2 最大公约数</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-6-1-3-%E6%AC%A7%E6%8B%89%E5%87%BD%E6%95%B0"><span class="nav-number">1.3.</span> <span class="nav-text">Part 6.1.3 欧拉函数</span></a></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-6-2-%E5%90%8C%E4%BD%99%E6%96%B9%E7%A8%8B"><span class="nav-number">2.</span> <span class="nav-text">Part 6.2 同余方程</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-6-2-1-%E7%BA%BF%E6%80%A7%E5%90%8C%E4%BD%99%E6%96%B9%E7%A8%8B-amp-%E4%B9%98%E6%B3%95%E9%80%86%E5%85%83"><span class="nav-number">2.1.</span> <span class="nav-text">Part 6.2.1 线性同余方程&amp;乘法逆元</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-6-2-2-%E4%B8%AD%E5%9B%BD%E5%89%A9%E4%BD%99%E5%AE%9A%E7%90%86"><span class="nav-number">2.2.</span> <span class="nav-text">Part 6.2.2 中国剩余定理</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-6-2-3-BSGS"><span class="nav-number">2.3.</span> <span class="nav-text">Part 6.2.3 BSGS</span></a></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-6-3-%E5%8D%9A%E5%BC%88%E8%AE%BA"><span class="nav-number">3.</span> <span class="nav-text">Part 6.3 博弈论</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-6-4-%E6%A6%82%E7%8E%87%E4%B8%8E%E6%9C%9F%E6%9C%9B"><span class="nav-number">4.</span> <span class="nav-text">Part 6.4 概率与期望</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-6-5-%E7%BB%84%E5%90%88%E6%95%B0%E5%AD%A6"><span class="nav-number">5.</span> <span class="nav-text">Part 6.5 组合数学</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-6-5-1-%E6%8E%92%E5%88%97%E7%BB%84%E5%90%88"><span class="nav-number">5.1.</span> <span class="nav-text">Part 6.5.1 排列组合</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-6-5-2-%E5%8D%A1%E7%89%B9%E5%85%B0%E6%95%B0-amp-%E6%96%AF%E7%89%B9%E6%9E%97%E6%95%B0"><span class="nav-number">5.2.</span> <span class="nav-text">Part 6.5.2 卡特兰数&amp;斯特林数</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-6-5-3-%E5%AE%B9%E6%96%A5%E5%8E%9F%E7%90%86"><span class="nav-number">5.3.</span> <span class="nav-text">Part 6.5.3 容斥原理</span></a></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-6-6-%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0"><span class="nav-number">6.</span> <span class="nav-text">Part 6.6 线性代数</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-6-6-1-%E7%9F%A9%E9%98%B5"><span class="nav-number">6.1.</span> <span class="nav-text">Part 6.6.1 矩阵</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-6-6-2-%E9%AB%98%E6%96%AF%E6%B6%88%E5%85%83"><span class="nav-number">6.2.</span> <span class="nav-text">Part 6.6.2 高斯消元</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-6-6-3-%E7%BA%BF%E6%80%A7%E5%9F%BA"><span class="nav-number">6.3.</span> <span class="nav-text">Part 6.6.3 线性基</span></a></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-6-7-%E5%A4%9A%E9%A1%B9%E5%BC%8F"><span class="nav-number">7.</span> <span class="nav-text">Part 6.7 多项式</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-6-8-%E8%8E%AB%E6%AF%94%E4%B9%8C%E6%96%AF%E5%8F%8D%E6%BC%94"><span class="nav-number">8.</span> <span class="nav-text">Part 6.8 莫比乌斯反演</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Part-7-%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84"><span class="nav-number"></span> <span class="nav-text">Part 7 数据结构</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-1-%E9%93%BE%E8%A1%A8"><span class="nav-number">1.</span> <span class="nav-text">Part 7.1 链表</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-2-%E6%A0%88"><span class="nav-number">2.</span> <span class="nav-text">Part 7.2 栈</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-3-%E9%98%9F%E5%88%97"><span class="nav-number">3.</span> <span class="nav-text">Part 7.3 队列</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-4-%E5%B9%B6%E6%9F%A5%E9%9B%86"><span class="nav-number">4.</span> <span class="nav-text">Part 7.4 并查集</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-5-%E5%A0%86"><span class="nav-number">5.</span> <span class="nav-text">Part 7.5 堆</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-6-%E6%A0%91%E7%8A%B6%E6%95%B0%E7%BB%84"><span class="nav-number">6.</span> <span class="nav-text">Part 7.6 树状数组</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-7-%E7%BA%BF%E6%AE%B5%E6%A0%91"><span class="nav-number">7.</span> <span class="nav-text">Part 7.7 线段树</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-8-%E5%88%86%E5%9D%97"><span class="nav-number">8.</span> <span class="nav-text">Part 7.8 分块</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-9-%E7%82%B9%E5%88%86%E6%B2%BB"><span class="nav-number">9.</span> <span class="nav-text">Part 7.9 点分治</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-10-%E4%B8%BB%E5%B8%AD%E6%A0%91"><span class="nav-number">10.</span> <span class="nav-text">Part 7.10 主席树</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-11-%E5%B9%B3%E8%A1%A1%E6%A0%91"><span class="nav-number">11.</span> <span class="nav-text">Part 7.11 平衡树</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-12-%E6%A0%91%E9%93%BE%E5%89%96%E5%88%86"><span class="nav-number">12.</span> <span class="nav-text">Part 7.12 树链剖分</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-13-%E6%A0%91%E5%A5%97%E6%A0%91"><span class="nav-number">13.</span> <span class="nav-text">Part 7.13 树套树</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-14-%E5%8A%A8%E6%80%81%E6%A0%91"><span class="nav-number">14.</span> <span class="nav-text">Part 7.14 动态树</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-15-CDQ%E5%88%86%E6%B2%BB-amp-%E6%95%B4%E4%BD%93%E4%BA%8C%E5%88%86"><span class="nav-number">15.</span> <span class="nav-text">Part 7.15 CDQ分治&amp;整体二分</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-7-16-%E5%8F%AF%E6%8C%81%E4%B9%85%E5%8C%96%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84"><span class="nav-number">16.</span> <span class="nav-text">Part 7.16 可持久化数据结构</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Part-8-%E5%9B%BE%E8%AE%BA"><span class="nav-number"></span> <span class="nav-text">Part 8 图论</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-8-1-%E5%9B%BE%E7%9A%84%E5%AD%98%E5%82%A8%E4%B8%8E%E9%81%8D%E5%8E%86"><span class="nav-number">1.</span> <span class="nav-text">Part 8.1 图的存储与遍历</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-8-2-%E6%9C%80%E7%9F%AD%E8%B7%AF%E9%97%AE%E9%A2%98"><span class="nav-number">2.</span> <span class="nav-text">Part 8.2 最短路问题</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-8-3-%E6%A0%91%E4%B8%8A%E9%97%AE%E9%A2%98"><span class="nav-number">3.</span> <span class="nav-text">Part 8.3 树上问题</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-8-3-1-%E4%BA%8C%E5%8F%89%E6%A0%91"><span class="nav-number">3.1.</span> <span class="nav-text">Part 8.3.1 二叉树</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-8-3-2-%E6%A0%91%E7%9A%84%E7%9B%B4%E5%BE%84"><span class="nav-number">3.2.</span> <span class="nav-text">Part 8.3.2 树的直径</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-8-3-3-%E6%9C%80%E8%BF%91%E5%85%AC%E5%85%B1%E7%A5%96%E5%85%88"><span class="nav-number">3.3.</span> <span class="nav-text">Part 8.3.3 最近公共祖先</span></a></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-8-4-%E7%94%9F%E6%88%90%E6%A0%91"><span class="nav-number">4.</span> <span class="nav-text">Part 8.4 生成树</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-8-5-%E6%8B%93%E6%89%91%E6%8E%92%E5%BA%8F"><span class="nav-number">5.</span> <span class="nav-text">Part 8.5 拓扑排序</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-8-6-%E5%B7%AE%E5%88%86%E7%BA%A6%E6%9D%9F"><span class="nav-number">6.</span> <span class="nav-text">Part 8.6 差分约束</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-8-7-%E5%9B%BE%E7%9A%84%E8%BF%9E%E9%80%9A%E6%80%A7%E7%9B%B8%E5%85%B3"><span class="nav-number">7.</span> <span class="nav-text">Part 8.7 图的连通性相关</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-8-8-%E4%BA%8C%E5%88%86%E5%9B%BE"><span class="nav-number">8.</span> <span class="nav-text">Part 8.8 二分图</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-8-9-%E7%BD%91%E7%BB%9C%E6%B5%81"><span class="nav-number">9.</span> <span class="nav-text">Part 8.9 网络流</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-8-9-1-%E6%9C%80%E5%A4%A7%E6%B5%81-%E6%9C%80%E5%B0%8F%E5%89%B2"><span class="nav-number">9.1.</span> <span class="nav-text">Part 8.9.1 最大流&#x2F;最小割</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-8-9-2-%E8%B4%B9%E7%94%A8%E6%B5%81"><span class="nav-number">9.2.</span> <span class="nav-text">Part 8.9.2 费用流</span></a></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-8-10-2-SAT"><span class="nav-number">10.</span> <span class="nav-text">Part 8.10 2-SAT</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-8-11-%E8%99%9A%E6%A0%91"><span class="nav-number">11.</span> <span class="nav-text">Part 8.11 虚树</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-8-12-%E7%9F%A9%E9%98%B5%E6%A0%91%E5%AE%9A%E7%90%86"><span class="nav-number">12.</span> <span class="nav-text">Part 8.12 矩阵树定理</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Part-9-%E8%AE%A1%E7%AE%97%E5%87%A0%E4%BD%95"><span class="nav-number"></span> <span class="nav-text">Part 9 计算几何</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-9-1-%E5%87%B8%E5%8C%85"><span class="nav-number">1.</span> <span class="nav-text">Part 9.1 凸包</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-9-2-%E6%97%8B%E8%BD%AC%E5%8D%A1%E5%A3%B3"><span class="nav-number">2.</span> <span class="nav-text">Part 9.2 旋转卡壳</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-9-3-%E5%8D%8A%E5%B9%B3%E9%9D%A2%E4%BA%A4"><span class="nav-number">3.</span> <span class="nav-text">Part 9.3 半平面交</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Part-10-%E6%9D%82%E9%A1%B9"><span class="nav-number"></span> <span class="nav-text">Part 10 杂项</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-10-1-%E6%A8%A1%E6%8B%9F%E9%80%80%E7%81%AB"><span class="nav-number">1.</span> <span class="nav-text">Part 10.1 模拟退火</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-10-2-0-1-%E5%88%86%E6%95%B0%E8%A7%84%E5%88%92"><span class="nav-number">2.</span> <span class="nav-text">Part 10.2 0&#x2F;1 分数规划</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-10-3-%E5%A5%87%E6%80%AA%E7%9A%84%E9%A2%98%E7%9B%AE"><span class="nav-number">3.</span> <span class="nav-text">Part 10.3 奇怪的题目</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Part-10-4-%E9%9D%9E%E4%BC%A0%E7%BB%9F%E9%A2%98"><span class="nav-number">4.</span> <span class="nav-text">Part 10.4 非传统题</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#Part-10-4-1-%E6%8F%90%E4%BA%A4%E7%AD%94%E6%A1%88%E9%A2%98"><span class="nav-number">4.1.</span> <span class="nav-text">Part 10.4.1 提交答案题</span></a></li></ol></li></ol></div>
      </section>
      <!--/noindex-->

      <section class="site-overview-wrap sidebar-panel">
        <div class="site-author animated" itemprop="author" itemscope itemtype="http://schema.org/Person">
    <img class="site-author-image" itemprop="image" alt="舒雨墨"
      src="/images/avatar.jpg">
  <p class="site-author-name" itemprop="name">舒雨墨</p>
  <div class="site-description" itemprop="description"></div>
</div>
<div class="site-state-wrap animated">
  <nav class="site-state">
      <div class="site-state-item site-state-posts">
          <a href="/archives/">
        
          <span class="site-state-item-count">106</span>
          <span class="site-state-item-name">日志</span>
        </a>
      </div>
      <div class="site-state-item site-state-categories">
        <span class="site-state-item-count">28</span>
        <span class="site-state-item-name">分类</span>
      </div>
      <div class="site-state-item site-state-tags">
            <a href="/tags/">
          
        <span class="site-state-item-count">53</span>
        <span class="site-state-item-name">标签</span></a>
      </div>
  </nav>
</div>
  <div class="links-of-author animated">
      <span class="links-of-author-item">
        <a href="https://github.com/ShuYuMo2003" title="GitHub → https:&#x2F;&#x2F;github.com&#x2F;ShuYuMo2003" rel="noopener" target="_blank"><i class="fab fa-github fa-fw"></i>GitHub</a>
      </span>
      <span class="links-of-author-item">
        <a href="https://www.luogu.com.cn/user/44615" title="Luogu → https:&#x2F;&#x2F;www.luogu.com.cn&#x2F;user&#x2F;44615" rel="noopener" target="_blank"><i class="fab fa-github fa-fw"></i>Luogu</a>
      </span>
      <span class="links-of-author-item">
        <a href="mailto:sujiayi2003@gmail.com" title="E-Mail → mailto:sujiayi2003@gmail.com" rel="noopener" target="_blank"><i class="fa fa-envelope fa-fw"></i>E-Mail</a>
      </span>
      <span class="links-of-author-item">
        <a href="https://twitter.com/JiaYiSu5" title="Twitter → https:&#x2F;&#x2F;twitter.com&#x2F;JiaYiSu5" rel="noopener" target="_blank"><i class="fab fa-twitter fa-fw"></i>Twitter</a>
      </span>
  </div>



      </section>
    </div>
  </aside>
  <div class="sidebar-dimmer"></div>


    </header>

    
  <div class="back-to-top">
    <i class="fa fa-arrow-up"></i>
    <span>0%</span>
  </div>

<noscript>
  <div class="noscript-warning">Theme NexT works best with JavaScript enabled</div>
</noscript>


    <div class="main-inner post posts-expand">
      

      

    
  
  
  <article itemscope itemtype="http://schema.org/Article" class="post-block" lang="zh-CN">
    <link itemprop="mainEntityOfPage" href="/2019/做题计划/">

    <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
      <meta itemprop="image" content="/images/avatar.jpg">
      <meta itemprop="name" content="舒雨墨">
      <meta itemprop="description" content="">
    </span>

    <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
      <meta itemprop="name" content="Shu Yu Mo's blog">
    </span>

    
    
      <header class="post-header">
        <h1 class="post-title" itemprop="name headline">
          做题计划
        </h1>

        <div class="post-meta-container">
          <div class="post-meta">
    <span class="post-meta-item">
      <span class="post-meta-item-icon">
        <i class="far fa-calendar"></i>
      </span>
      <span class="post-meta-item-text">发表于</span>

      <time title="创建时间：2019-06-24 08:06:00" itemprop="dateCreated datePublished" datetime="2019-06-24T08:06:00+08:00">2019-06-24</time>
    </span>
      <span class="post-meta-item">
        <span class="post-meta-item-icon">
          <i class="far fa-calendar-check"></i>
        </span>
        <span class="post-meta-item-text">更新于</span>
        <time title="修改时间：2020-09-05 11:46:40" itemprop="dateModified" datetime="2020-09-05T11:46:40+08:00">2020-09-05</time>
      </span>

  
    <span id="2019/做题计划/" class="post-meta-item leancloud_visitors" data-flag-title="做题计划" title="阅读次数">
      <span class="post-meta-item-icon">
        <i class="far fa-eye"></i>
      </span>
      <span class="post-meta-item-text">阅读次数：</span>
      <span class="leancloud-visitors-count"></span>
    </span>
  
  <span class="post-meta-item">
    
      <span class="post-meta-item-icon">
        <i class="far fa-comment"></i>
      </span>
      <span class="post-meta-item-text">Valine：</span>
    
    <a title="valine" href="/2019/做题计划/#valine-comments" itemprop="discussionUrl">
      <span class="post-comments-count valine-comment-count" data-xid="2019/做题计划/" itemprop="commentCount"></span>
    </a>
  </span>
  
  
      </div>
      <div class="post-meta">
    <span class="post-meta-item" title="本文字数">
      <span class="post-meta-item-icon">
        <i class="far fa-file-word"></i>
      </span>
      <span class="post-meta-item-text">本文字数：</span>
      <span>13k</span>
    </span>
    <span class="post-meta-item" title="阅读时长">
      <span class="post-meta-item-icon">
        <i class="far fa-clock"></i>
      </span>
      <span class="post-meta-item-text">阅读时长 &asymp;</span>
      <span>11 分钟</span>
    </span>
</div>

        </div>
      </header>

    
    
    
    <div class="post-body" itemprop="articleBody">
        <h3 id="Part-2-1-模拟"><a href="#Part-2-1-模拟" class="headerlink" title="Part 2.1 模拟"></a>Part 2.1 模拟</h3><ul>
<li>[P2482 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2482">SDOI2010]猪国杀</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3693">P3693 琪露诺的冰雪小屋</a></li>
<li>[P5380 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5380">THUPC2019]鸭棋</a></li>
</ul>
<h3 id="Part-2-2-排序算法"><a href="#Part-2-2-排序算法" class="headerlink" title="Part 2.2 排序算法"></a>Part 2.2 排序算法</h3><a id="more"></a>

<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1908">P1908 逆序对</a></li>
</ul>
<h3 id="Part-2-3-二分答案"><a href="#Part-2-3-二分答案" class="headerlink" title="Part 2.3 二分答案"></a>Part 2.3 二分答案</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2678">P2678 跳石头</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1316">P1316 丢瓶盖</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1902">P1902 刺杀大使</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1314">P1314 聪明的质监员</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1083">P1083 借教室</a></li>
<li>[P4343 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4343">SHOI2015]自动刷题机</a></li>
</ul>
<h3 id="Part-2-4-分治"><a href="#Part-2-4-分治" class="headerlink" title="Part 2.4 分治"></a>Part 2.4 分治</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1257">P1257 平面上的最接近点对</a></li>
<li>[P3612 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3612">USACO17JAN]Secret Cow Code秘密奶牛码</a></li>
</ul>
<h3 id="Part-2-5-贪心"><a href="#Part-2-5-贪心" class="headerlink" title="Part 2.5 贪心"></a>Part 2.5 贪心</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1090"><del>P1090 合并果子</del></a></li>
<li>[P1208 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1208">USACO1.3]混合牛奶 Mixing Milk</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1094">P1094 纪念品分组</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1199">P1199 三国游戏</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2672">P2672 推销员</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1080"><del>P1080 国王游戏</del></a></li>
</ul>
<h3 id="Part-2-6-高精度"><a href="#Part-2-6-高精度" class="headerlink" title="Part 2.6 高精度"></a>Part 2.6 高精度</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1601">P1601 A+B Problem（高精）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2142">P2142 高精度减法</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1303">P1303 A*B Problem</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1480">P1480 A/B Problem</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1009">P1009 阶乘之和</a></li>
</ul>
<h2 id="Part-3-搜索"><a href="#Part-3-搜索" class="headerlink" title="Part 3 搜索"></a>Part 3 搜索</h2><h3 id="Part-3-1-深度优先搜索"><a href="#Part-3-1-深度优先搜索" class="headerlink" title="Part 3.1 深度优先搜索"></a>Part 3.1 深度优先搜索</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1019">P1019 单词接龙</a></li>
<li>[P5194 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5194">USACO05DEC]Scales 天平</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1378">P1378 油滴扩展</a></li>
</ul>
<h3 id="Part-3-2-广度优先搜索"><a href="#Part-3-2-广度优先搜索" class="headerlink" title="Part 3.2 广度优先搜索"></a>Part 3.2 广度优先搜索</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1032">P1032 字串变换</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1126">P1126 机器人搬重物</a></li>
</ul>
<h3 id="Part-3-3-记忆化搜索"><a href="#Part-3-3-记忆化搜索" class="headerlink" title="Part 3.3 记忆化搜索"></a>Part 3.3 记忆化搜索</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1535">P1535 游荡的奶牛</a></li>
<li>[P1434 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1434">SHOI2002]滑雪</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3953">P3953 逛公园</a></li>
</ul>
<h3 id="Part-3-4-搜索的剪枝"><a href="#Part-3-4-搜索的剪枝" class="headerlink" title="Part 3.4 搜索的剪枝"></a>Part 3.4 搜索的剪枝</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1120"><del>P1120 小木棍 ［数据加强版］</del></a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1312">P1312 Mayan游戏</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1074">P1074 靶形数独</a></li>
</ul>
<h3 id="Part-3-5-双向搜索"><a href="#Part-3-5-双向搜索" class="headerlink" title="Part 3.5 双向搜索"></a>Part 3.5 双向搜索</h3><blockquote>
<p>在搜索时，如果能从初态和终态出发，同时进行搜索，就可以减小搜索树的规模，提高时间效率。</p>
</blockquote>
<ul>
<li>[P3067 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3067">USACO12OPEN]Balanced Cow Subsets</a></li>
<li>[P4799 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4799">CEOI2015 Day2]世界冰球锦标赛</a></li>
<li>[P5195 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5195">USACO05DEC]Knights of Ni 骑士</a></li>
</ul>
<h3 id="Part-3-6-A"><a href="#Part-3-6-A" class="headerlink" title="Part 3.6 A*"></a>Part 3.6 A*</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1379">P1379 八数码难题</a></li>
</ul>
<h3 id="Part-3-7-IDA"><a href="#Part-3-7-IDA" class="headerlink" title="Part 3.7 IDA*"></a>Part 3.7 IDA*</h3><blockquote>
<p>像 BFS 那样，每次只扩展一层节点，却采用 DFS 方式来遍历搜索树，这就是迭代加深搜索。</p>
<p>再加上一个估价函数来减小搜索量，就是 IDA*了。</p>
</blockquote>
<ul>
<li>[P2324 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2324">SCOI2005]骑士精神</a></li>
</ul>
<h2 id="Part-4-动态规划"><a href="#Part-4-动态规划" class="headerlink" title="Part 4 动态规划"></a>Part 4 动态规划</h2><blockquote>
<p>动态规划是一种重要的思维方法，通过利用已有的子问题信息高效求出当前问题的最优解。</p>
</blockquote>
<h3 id="Part-4-1-线性动态规划"><a href="#Part-4-1-线性动态规划" class="headerlink" title="Part 4.1 线性动态规划"></a>Part 4.1 线性动态规划</h3><blockquote>
<p>线性动态规划，即具有线性阶段划分的动态规划。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1216">P1216 数字三角形</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1020">P1020 导弹拦截</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1091">P1091 合唱队形</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1095">P1095 守望者的逃离</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1541">P1541 乌龟棋</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1868">P1868 饥饿的奶牛</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2679">P2679 子串</a></li>
<li>[P2501 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2501">HAOI2006]数字序列</a></li>
<li>[P3336 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3336">ZJOI2013]话旧</a></li>
<li>[P3558 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3558">POI2013]BAJ-Bytecomputer</a></li>
<li>[P4158 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4158">SCOI2009]粉刷匠</a></li>
<li>[P5301 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5301">GXOI/GZOI2019]宝牌一大堆</a></li>
</ul>
<h3 id="Part-4-2-背包动态规划"><a href="#Part-4-2-背包动态规划" class="headerlink" title="Part 4.2 背包动态规划"></a>Part 4.2 背包动态规划</h3><blockquote>
<p>背包动态规划是线性动态规划中特殊的一类，NOIP中考到的次数也不少。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1048">P1048 采药</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1060">P1060 开心的金明</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1855">P1855 榨取kkksc03</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5020">P5020 货币系统</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1064">P1064 金明的预算方案</a></li>
<li>[P2946 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2946">USACO09MAR]牛飞盘队Cow Frisbee Team</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1156">P1156 垃圾陷阱</a></li>
<li>[P5322 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5322">BJOI2019]排兵布阵</a></li>
<li>[P5289 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5289">十二省联考2019]皮配</a></li>
</ul>
<h3 id="Part-4-3-区间动态规划"><a href="#Part-4-3-区间动态规划" class="headerlink" title="Part 4.3 区间动态规划"></a>Part 4.3 区间动态规划</h3><blockquote>
<p>区间动态规划一般以区间作为动态规划的阶段。</p>
</blockquote>
<ul>
<li>[P1880 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1880">NOI1995]石子合并</a></li>
<li>[P3146 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3146">USACO16OPEN]248</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1063">P1063 能量项链</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1005">P1005 矩阵取数游戏</a></li>
<li>[P4170 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4170">CQOI2007]涂色</a></li>
<li>[P4302 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4302">SCOI2003]字符串折叠</a></li>
<li>[P2466 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2466">SDOI2008]Sue的小球</a></li>
</ul>
<h3 id="Part-4-4-树形动态规划"><a href="#Part-4-4-树形动态规划" class="headerlink" title="Part 4.4 树形动态规划"></a>Part 4.4 树形动态规划</h3><blockquote>
<p>树形动态规划，即在树上进行的动态规划。</p>
<p>因为树的递归性质，树形动态规划一般都是递归求解的。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1352">P1352 没有上司的舞会</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1040">P1040 加分二叉树</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1122">P1122 最大子树和</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1270">P1270 “访问”美术馆</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1273">P1273 有线电视网</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2014">P2014 选课</a></li>
<li>[P3177 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3177">HAOI2015]树上染色</a></li>
<li>[P4516 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4516">JSOI2018]潜入行动</a></li>
</ul>
<h3 id="Part-4-5-状态压缩动态规划"><a href="#Part-4-5-状态压缩动态规划" class="headerlink" title="Part 4.5 状态压缩动态规划"></a>Part 4.5 状态压缩动态规划</h3><blockquote>
<p>将一个状态压缩为一个整数（通常为二进制数），就可以在更为方便地进行状态转移的同时，达到节约空间的目的。</p>
</blockquote>
<ul>
<li>[<del>P2704 [NOI2001]炮兵阵地</del>](<a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2704">https://www.luogu.org/problemnew/show/P2704</a>)</li>
<li>[P1879 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1879">USACO06NOV]玉米田Corn Fields</a></li>
<li>[<del>P1896 [SCOI2005]互不侵犯</del>](<a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1896">https://www.luogu.org/problemnew/show/P1896</a>)</li>
<li>[P3092 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3092">USACO13NOV]没有找零No Change</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3694">P3694 邦邦的大合唱站队</a></li>
<li>[P4925 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4925">1007]Scarlet的字符串不可能这么可爱</a></li>
<li>[P3648 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3648">APIO2014]序列分割</a></li>
<li>[P2157 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2157">SDOI2009]学校食堂</a></li>
<li>[P2167 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2167">SDOI2009]Bill的挑战</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2396">P2396 yyy loves Maths VII</a></li>
<li>[P4363 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4363">九省联考2018]一双木棋chess</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5005">P5005 中国象棋 – 摆上马</a></li>
<li>[P2150 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2150">NOI2015]寿司晚宴</a></li>
</ul>
<h3 id="Part-4-6-倍增优化动态规划"><a href="#Part-4-6-倍增优化动态规划" class="headerlink" title="Part 4.6 倍增优化动态规划"></a>Part 4.6 倍增优化动态规划</h3><blockquote>
<p>利用倍增的方式，我们可以将状态转移的效率大大提高。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1613">P1613 跑路</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1081">P1081 开车旅行</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5024">P5024 保卫王国</a></li>
</ul>
<h3 id="Part-4-7-数据结构优化动态规划"><a href="#Part-4-7-数据结构优化动态规划" class="headerlink" title="Part 4.7 数据结构优化动态规划"></a>Part 4.7 数据结构优化动态规划</h3><blockquote>
<p>利用数据结构来维护已有信息，也可以达到优化状态转移的目的。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4719">P4719 【模板】动态dp</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4751">P4751 动态dp【加强版】</a></li>
<li>[P3287 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3287">SCOI2014]方伯伯的玉米田</a></li>
<li>[P2605 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2605">ZJOI2010]基站选址</a></li>
</ul>
<h3 id="Part-4-8-单调队列优化动态规划"><a href="#Part-4-8-单调队列优化动态规划" class="headerlink" title="Part 4.8 单调队列优化动态规划"></a>Part 4.8 单调队列优化动态规划</h3><blockquote>
<p>如果决策具有单调性，就可以考虑运用单调队列来优化动态规划的效率。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1776">P1776 宝物筛选_NOI导刊2010提高（02）</a></li>
<li>[P3089 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3089">USACO13NOV]POGO的牛Pogo-Cow</a></li>
<li>[P3572 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3572">POI2014]PTA-Little Bird</a></li>
<li>[P3522 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3522">POI2011]TEM-Temperature</a></li>
<li>[P4544 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4544">USACO10NOV]购买饲料Buying Feed</a></li>
<li>[P1973 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1973">NOI2011]Noi嘉年华</a></li>
<li>[P2569 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2569">SCOI2010]股票交易</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4852">P4852 yyf hates choukapai</a></li>
</ul>
<h3 id="Part-4-9-斜率优化动态规划"><a href="#Part-4-9-斜率优化动态规划" class="headerlink" title="Part 4.9 斜率优化动态规划"></a>Part 4.9 斜率优化动态规划</h3><blockquote>
<p>通过用单调队列维护一个凸壳，来达到优化转移的目的。</p>
</blockquote>
<ul>
<li>[P2305 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2305">NOI2014]购票</a></li>
<li>[P2900 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2900">USACO08MAR]土地征用Land Acquisition</a></li>
<li>[P3195 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3195">HNOI2008]玩具装箱TOY</a></li>
<li>[P3628 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3628">APIO2010]特别行动队</a></li>
<li>[P4027 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4027">NOI2007]货币兑换</a></li>
<li>[P4360 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4360">CEOI2004]锯木厂选址</a></li>
</ul>
<h3 id="Part-4-10-四边形不等式优化动态规划"><a href="#Part-4-10-四边形不等式优化动态规划" class="headerlink" title="Part 4.10 四边形不等式优化动态规划"></a>Part 4.10 四边形不等式优化动态规划</h3><blockquote>
<p>利用四边形不等式，我们就可以提高一些区间动态规划的效率。</p>
</blockquote>
<ul>
<li>P3515 [POI2011]Lightning Conductor</li>
</ul>
<ul>
<li>[P4767 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4767">IOI2000]邮局</a></li>
</ul>
<h3 id="Part-4-11-数位统计类动态规划"><a href="#Part-4-11-数位统计类动态规划" class="headerlink" title="Part 4.11 数位统计类动态规划"></a>Part 4.11 数位统计类动态规划</h3><blockquote>
<p>统计一个区间中满足条件的数有多少，就是数位统计类动态规划。</p>
</blockquote>
<ul>
<li>[P2602 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2602">ZJOI2010]数字计数</a></li>
<li>[P3281 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3281">SCOI2013]数数</a></li>
<li>[P2518 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2518">HAOI2010]计数</a></li>
<li>[P2657 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2657">SCOI2009]windy数</a></li>
<li>[P3286 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3286">SCOI2014]方伯伯的商场之旅</a></li>
<li>[P4124 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4124">CQOI2016]手机号码</a></li>
<li>[P2606 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2606">ZJOI2010]排列计数</a></li>
</ul>
<h3 id="Part-4-12-轮廓线动态规划"><a href="#Part-4-12-轮廓线动态规划" class="headerlink" title="Part 4.12 轮廓线动态规划"></a>Part 4.12 轮廓线动态规划</h3><blockquote>
<p>轮廓线动态规划（即常说的插头 DP）是一种特殊的状压动态规划，通过以轮廓线为状态来实现状态转移。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5056">P5056 【模板】插头dp</a></li>
<li>[P2289 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2289">HNOI2004]邮递员</a></li>
<li>[P2337 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2337">SCOI2012]喵星人的入侵</a></li>
</ul>
<h2 id="Part-5-字符串"><a href="#Part-5-字符串" class="headerlink" title="Part 5 字符串"></a>Part 5 字符串</h2><blockquote>
<p>字符串问题有很多自己的特点。</p>
</blockquote>
<h3 id="Part-5-1-字符串哈希"><a href="#Part-5-1-字符串哈希" class="headerlink" title="Part 5.1 字符串哈希"></a>Part 5.1 字符串哈希</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3370">P3370 【模板】字符串哈希</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5270">P5270 无论怎样神树大人都会删库跑路</a></li>
</ul>
<h3 id="Part-5-2-KMP"><a href="#Part-5-2-KMP" class="headerlink" title="Part 5.2 KMP"></a>Part 5.2 KMP</h3><blockquote>
<p>KMP 算法可以用来解决模式串匹配问题。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3375">P3375 【模板】KMP字符串匹配</a></li>
<li>[P4391 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4391">BOI2009]Radio Transmission 无线传输</a></li>
<li>[P3435 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3435">POI2006]OKR-Periods of Words</a></li>
<li>[P2375 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2375">NOI2014]动物园</a></li>
<li>[P3426 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3426">POI2005]SZA-Template</a></li>
<li>[P3193 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3193">HNOI2008]GT考试</a></li>
<li>[P3435 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3435">POI2006]OKR-Periods of Words</a></li>
</ul>
<h3 id="Part-5-3-Manacher"><a href="#Part-5-3-Manacher" class="headerlink" title="Part 5.3 Manacher"></a>Part 5.3 Manacher</h3><blockquote>
<p>Manacher 可以在线性时间内求出一个字符串的最长回文子串。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3805">P3805 【模板】manacher算法</a></li>
<li>[P4555 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4555">国家集训队]最长双回文串</a></li>
<li>[P1659 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1659">国家集训队]拉拉队排练</a></li>
</ul>
<h3 id="Part-5-4-Trie树"><a href="#Part-5-4-Trie树" class="headerlink" title="Part 5.4 Trie树"></a>Part 5.4 Trie树</h3><ul>
<li>[P3879 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3879">TJOI2010]阅读理解</a></li>
<li>[P2292 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2292">HNOI2004]L语言</a></li>
<li>[P2922 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2922">USACO08DEC]秘密消息Secret Message</a></li>
<li>[P3065 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3065">USACO12DEC]第一!First!</a></li>
<li>[P3294 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3294">SCOI2016]背单词</a></li>
<li>[P4407 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4407">JSOI2009]电子字典</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4551">P4551 最长异或路径</a></li>
<li>[P4683 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4683">IOI2008] Type Printer 打印机</a></li>
<li>[P3783 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3783">SDOI2017]天才黑客</a></li>
</ul>
<h3 id="Part-5-5-AC自动机"><a href="#Part-5-5-AC自动机" class="headerlink" title="Part 5.5 AC自动机"></a>Part 5.5 AC自动机</h3><blockquote>
<p>AC自动机可以看成是 KMP 和 Trie 的结合体，用于解决多字符串匹配问题。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3808">P3808 【模板】AC自动机（简单版）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3796">P3796 【模板】AC自动机（加强版）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5357">P5357 【模板】AC自动机（二次加强版）</a></li>
<li>[P3121 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3121">USACO15FEB]审查（黄金）Censoring (Gold)</a></li>
<li>[P2414 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2414">NOI2011]阿狸的打字机</a></li>
<li>[P3966 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3966">TJOI2013]单词</a></li>
<li>[P2444 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2444">POI2000]病毒</a></li>
<li>[P3311 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3311">SDOI2014]数数</a></li>
<li>[P4052 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4052">JSOI2007]文本生成器</a></li>
</ul>
<h3 id="Part-5-6-后缀数组"><a href="#Part-5-6-后缀数组" class="headerlink" title="Part 5.6 后缀数组"></a>Part 5.6 后缀数组</h3><blockquote>
<p>后缀数组是处理字符串的有力工具。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3809">P3809 【模板】后缀排序</a></li>
<li>[P1117 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1117">NOI2016]优秀的拆分</a></li>
<li>[P2178 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2178">NOI2015]品酒大会</a></li>
<li>[P2463 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2463">SDOI2008]Sandy的卡片</a></li>
<li>[P4051 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4051">JSOI2007]字符加密</a></li>
<li>[P2336 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2336">SCOI2012]喵星球上的点名</a></li>
<li>[P2852 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2852">USACO06DEC]牛奶模式Milk Patterns</a></li>
<li>[P5319 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5319">BJOI2019]奥术神杖</a></li>
</ul>
<h3 id="Part-5-7-后缀自动机"><a href="#Part-5-7-后缀自动机" class="headerlink" title="Part 5.7 后缀自动机"></a>Part 5.7 后缀自动机</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3804">P3804 【模板】后缀自动机</a></li>
<li>[P3649 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3649">APIO2014]回文串</a></li>
<li>[P3975 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3975">TJOI2015]弦论</a></li>
<li>[P4248 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4248">AHOI2013]差异</a></li>
<li>[P5341 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5341">TJOI2019]甲苯先生和大中锋的字符串</a></li>
<li>[P4770 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4770">NOI2018]你的名字</a></li>
<li>[P5284 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5284">十二省联考2019]字符串问题</a></li>
</ul>
<h2 id="Part-6-数学"><a href="#Part-6-数学" class="headerlink" title="Part 6 数学"></a>Part 6 数学</h2><blockquote>
<p>OI 中的数学知识很多，也有些杂乱。</p>
</blockquote>
<h3 id="Part-6-1-整除相关"><a href="#Part-6-1-整除相关" class="headerlink" title="Part 6.1 整除相关"></a>Part 6.1 整除相关</h3><blockquote>
<p>与整除相关的概念有很多，比较常用的有素数，最大公约数和欧拉函数。</p>
</blockquote>
<h4 id="Part-6-1-1-素数"><a href="#Part-6-1-1-素数" class="headerlink" title="Part 6.1.1 素数"></a>Part 6.1.1 素数</h4><blockquote>
<p>素数，指的是除 1 和它本身之外没有其他约数的数。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3383">P3383 【模板】线性筛素数</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4718">P4718 【模板】Pollard-Rho算法</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1865">P1865 A % B Problem</a></li>
</ul>
<h4 id="Part-6-1-2-最大公约数"><a href="#Part-6-1-2-最大公约数" class="headerlink" title="Part 6.1.2 最大公约数"></a>Part 6.1.2 最大公约数</h4><blockquote>
<p>如果两个数有一个共同的约数，那么这个约数就被称为公约数。最大公约数就是指这两个数的所有公约数中，最大的一个。</p>
<p>求解两个数的最大公约数，可以采用欧几里得算法解决。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1029">P1029 最大公约数和最小公倍数问题</a></li>
<li>[P2152 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2152">SDOI2009]SuperGCD</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1072">P1072 Hankson 的趣味题</a></li>
</ul>
<h4 id="Part-6-1-3-欧拉函数"><a href="#Part-6-1-3-欧拉函数" class="headerlink" title="Part 6.1.3 欧拉函数"></a>Part 6.1.3 欧拉函数</h4><blockquote>
<p>欧拉函数 $ \varphi (x) $ 表示了小于 $ x $ 的数字中，与 $ x $ 互质的数字个数。</p>
</blockquote>
<ul>
<li>[P2158 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2158">SDOI2008]仪仗队</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2568">P2568 GCD</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2398">P2398 GCD SUM</a></li>
</ul>
<h3 id="Part-6-2-同余方程"><a href="#Part-6-2-同余方程" class="headerlink" title="Part 6.2 同余方程"></a>Part 6.2 同余方程</h3><blockquote>
<p>求解不定方程往往可以引出不少话题。</p>
</blockquote>
<h4 id="Part-6-2-1-线性同余方程-amp-乘法逆元"><a href="#Part-6-2-1-线性同余方程-amp-乘法逆元" class="headerlink" title="Part 6.2.1 线性同余方程&amp;乘法逆元"></a>Part 6.2.1 线性同余方程&amp;乘法逆元</h4><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4549">P4549 【模板】裴蜀定理</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2613">P2613 【模板】有理数取余</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1082">P1082 同余方程</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1414">P1414 又是毕业季II</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3951">P3951 小凯的疑惑</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1516">P1516 青蛙的约会</a></li>
</ul>
<h4 id="Part-6-2-2-中国剩余定理"><a href="#Part-6-2-2-中国剩余定理" class="headerlink" title="Part 6.2.2 中国剩余定理"></a>Part 6.2.2 中国剩余定理</h4><blockquote>
<p>中国剩余定理可以快速解一元线性同余方程组。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4777">P4777 【模板】扩展中国剩余定理（EXCRT）</a></li>
<li>[P3868 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3868">TJOI2009]猜数字</a></li>
<li>[P2480 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2480">SDOI2010]古代猪文</a></li>
<li>[P4774 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4774">NOI2018]屠龙勇士</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5345">P5345 【XR-1】快乐肥宅</a></li>
</ul>
<h4 id="Part-6-2-3-BSGS"><a href="#Part-6-2-3-BSGS" class="headerlink" title="Part 6.2.3 BSGS"></a>Part 6.2.3 BSGS</h4><blockquote>
<p>BSGS 算法可以高效计算高次同余方程的解。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4195">P4195 【模板】exBSGS/Spoj3105 Mod</a></li>
<li>[P3306 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3306">SDOI2013]随机数生成器</a></li>
</ul>
<h3 id="Part-6-3-博弈论"><a href="#Part-6-3-博弈论" class="headerlink" title="Part 6.3 博弈论"></a>Part 6.3 博弈论</h3><blockquote>
<p>博弈论考虑游戏中的个体的预测行为和实际行为，并研究它们的优化策略。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2197">P2197 【模板】nim游戏</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1288">P1288 取数游戏II</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1290">P1290 欧几里德的游戏</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1247">P1247 取火柴游戏</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2252">P2252 取石子游戏</a></li>
</ul>
<h3 id="Part-6-4-概率与期望"><a href="#Part-6-4-概率与期望" class="headerlink" title="Part 6.4 概率与期望"></a>Part 6.4 概率与期望</h3><blockquote>
<p>概率和期望是紧密相连的，OI 中往往会出现和概率期望相关的动态规划问题。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5104">P5104 红包发红包</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1837">P1837 单人纸牌_NOI导刊2011提高（04）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1850">P1850 换教室</a></li>
<li>[P3830 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3830">SHOI2012]随机树</a></li>
<li>[P4564 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4564">CTSC2018]假面</a></li>
<li>[P2473 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2473">SCOI2008]奖励关</a></li>
<li>[P2221 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2221">HAOI2012]高速公路</a></li>
<li>[P3750 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3750">六省联考2017]分手是祝愿</a></li>
<li>[P4284 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4284">SHOI2014]概率充电器</a></li>
<li>[P5249 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5249">LnOI2019]加特林轮盘赌</a></li>
<li>[P2081 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2081">NOI2012]迷失游乐园</a></li>
<li>[P3343 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3343">ZJOI2015]地震后的幻想乡</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3600">P3600 随机数生成器</a></li>
<li>[P5326 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5326">ZJOI2019]开关</a></li>
</ul>
<h3 id="Part-6-5-组合数学"><a href="#Part-6-5-组合数学" class="headerlink" title="Part 6.5 组合数学"></a>Part 6.5 组合数学</h3><h4 id="Part-6-5-1-排列组合"><a href="#Part-6-5-1-排列组合" class="headerlink" title="Part 6.5.1 排列组合"></a>Part 6.5.1 排列组合</h4><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3807">P3807 【模板】卢卡斯定理</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2822">P2822 组合数问题</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1655">P1655 小朋友的球</a></li>
<li>[P3197 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3197">HNOI2008]越狱</a></li>
<li>[P2290 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2290">HNOI2004]树的计数</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4981">P4981 父子</a></li>
<li>[P4769 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4769">NOI2018]冒泡排序</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4931">P4931 情侣？给我烧了！（加强版）</a></li>
</ul>
<h4 id="Part-6-5-2-卡特兰数-amp-斯特林数"><a href="#Part-6-5-2-卡特兰数-amp-斯特林数" class="headerlink" title="Part 6.5.2 卡特兰数&amp;斯特林数"></a>Part 6.5.2 卡特兰数&amp;斯特林数</h4><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5395">P5395 【模板】第二类斯特林数·行</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5396">P5396 【模板】第二类斯特林数·列</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5408">P5408 【模板】第一类斯特林数·行</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5409">P5409 【模板】第一类斯特林数·列</a></li>
<li>[P2532 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2532">AHOI2012]树屋阶梯</a></li>
<li>[P3200 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3200">HNOI2009]有趣的数列</a></li>
<li>[P3978 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3978">TJOI2015]概率论</a></li>
<li>[P4091 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4091">HEOI2016/TJOI2016]求和</a></li>
<li>[P4827 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4827">国家集训队] Crash 的文明世界</a></li>
</ul>
<h4 id="Part-6-5-3-容斥原理"><a href="#Part-6-5-3-容斥原理" class="headerlink" title="Part 6.5.3 容斥原理"></a>Part 6.5.3 容斥原理</h4><ul>
<li>[P1450 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1450">HAOI2008]硬币购物</a></li>
<li>[P3214 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3214">HNOI2011]卡农</a></li>
<li>[P3270 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3270">JLOI2016]成绩比较</a></li>
<li>[P4336 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4336">SHOI2016]黑暗前的幻想乡</a></li>
<li>[P4448 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4448">AHOI2018初中组]球球的排列</a></li>
<li>[P4491 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4491">HAOI2018]染色</a></li>
<li>[P5339 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5339">TJOI2019]唱、跳、rap和篮球</a></li>
<li>[P5400 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5400">CTS2019]随机立方体</a></li>
</ul>
<h3 id="Part-6-6-线性代数"><a href="#Part-6-6-线性代数" class="headerlink" title="Part 6.6 线性代数"></a>Part 6.6 线性代数</h3><h4 id="Part-6-6-1-矩阵"><a href="#Part-6-6-1-矩阵" class="headerlink" title="Part 6.6.1 矩阵"></a>Part 6.6.1 矩阵</h4><blockquote>
<p>利用矩阵优化数列递推，可以实现复杂度从线性到对数级的转变。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3390">P3390 【模板】矩阵快速幂</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1939">P1939 【模板】矩阵加速（数列）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4783">P4783 【模板】矩阵求逆</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1962">P1962 斐波那契数列</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1349">P1349 广义斐波那契数列</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4000">P4000 斐波那契数列</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5343">P5343 【XR-1】分块</a></li>
<li>[P5337 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5337">TJOI2019]甲苯先生的字符串</a></li>
<li>[P5303 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5303">GXOI/GZOI2019]逼死强迫症</a></li>
</ul>
<h4 id="Part-6-6-2-高斯消元"><a href="#Part-6-6-2-高斯消元" class="headerlink" title="Part 6.6.2 高斯消元"></a>Part 6.6.2 高斯消元</h4><blockquote>
<p>高斯消元可以用来求解方程组。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3389">P3389 【模板】高斯消元法</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4387">P4387 付公主的函数</a></li>
<li>[P4035 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4035">JSOI2008]球形空间产生器</a></li>
<li>[P4111 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4111">HEOI2015]小Z的房间</a></li>
<li>[P4457 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4457">BJOI2018]治疗之雨</a></li>
</ul>
<h4 id="Part-6-6-3-线性基"><a href="#Part-6-6-3-线性基" class="headerlink" title="Part 6.6.3 线性基"></a>Part 6.6.3 线性基</h4><blockquote>
<p>线性基可以求解最大异或和的一类问题。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3812">P3812 【模板】线性基</a></li>
<li>[P3857 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3857">TJOI2008]彩灯</a></li>
<li>[P4301 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4301">CQOI2013]新Nim游戏</a></li>
<li>[P3292 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3292">SCOI2016]幸运数字</a></li>
<li>[P4151 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4151">WC2011]最大XOR和路径</a></li>
</ul>
<h3 id="Part-6-7-多项式"><a href="#Part-6-7-多项式" class="headerlink" title="Part 6.7 多项式"></a>Part 6.7 多项式</h3><blockquote>
<p>对多项式的运算进行优化，从而能够解决规模更大的问题。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1919">P1919 【模板】A*B Problem升级版（FFT快速傅里叶）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3803">P3803 【模板】多项式乘法（FFT）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4238">P4238 【模板】多项式求逆</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4239">P4239 【模板】多项式求逆（加强版）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4245">P4245 【模板】任意模数NTT</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4717">P4717 【模板】快速沃尔什变换</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4721">P4721 【模板】分治 FFT</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4725">P4725 【模板】多项式对数函数</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4726">P4726 【模板】多项式指数函数</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4781">P4781 【模板】拉格朗日插值</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5050">P5050 【模板】多项式多点求值</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5158">P5158 【模板】多项式快速插值</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5205">P5205 【模板】多项式开根</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5245">P5245 【模板】多项式快速幂</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5264">P5264 【模板】多项式三角函数</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5265">P5265 【模板】多项式反三角函数</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5273">P5273 【模板】多项式幂函数 (加强版)</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5277">P5277 【模板】多项式开根（加强版）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5282">P5282 【模板】快速阶乘算法</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5373">P5373 【模板】多项式复合函数</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5383">P5383 【模板】普通多项式转下降幂多项式</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5393">P5393 【模板】下降幂多项式转普通多项式</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5394">P5394 【模板】下降幂多项式乘法</a></li>
<li>[P3338 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3338">ZJOI2014]力</a></li>
<li>[P3723 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3723">AH2017/HNOI2017]礼物</a></li>
<li>[P5293 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5293">HNOI2019]白兔之舞</a></li>
</ul>
<h3 id="Part-6-8-莫比乌斯反演"><a href="#Part-6-8-莫比乌斯反演" class="headerlink" title="Part 6.8 莫比乌斯反演"></a>Part 6.8 莫比乌斯反演</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3768">P3768 简单的数学题</a></li>
<li>[P3172 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3172">CQOI2015]选数</a></li>
<li>[P3455 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3455">POI2007]ZAP-Queries</a></li>
<li>[P3327 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3327">SDOI2015]约数个数和</a></li>
<li>[P4619 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4619">SDOI2018]旧试题</a></li>
</ul>
<h2 id="Part-7-数据结构"><a href="#Part-7-数据结构" class="headerlink" title="Part 7 数据结构"></a>Part 7 数据结构</h2><blockquote>
<p>灵活地运用数据结构可以高效地查询并处理需要的信息。</p>
</blockquote>
<h3 id="Part-7-1-链表"><a href="#Part-7-1-链表" class="headerlink" title="Part 7.1 链表"></a>Part 7.1 链表</h3><blockquote>
<p>在一个数列中高效插入一个元素，链表毫无疑问是最好的选择。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1996">P1996 约瑟夫问题</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1160">P1160 队列安排</a></li>
</ul>
<h3 id="Part-7-2-栈"><a href="#Part-7-2-栈" class="headerlink" title="Part 7.2 栈"></a>Part 7.2 栈</h3><blockquote>
<p>栈，是一种后进先出（FILO）的数据结构。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1449">P1449 后缀表达式</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1739">P1739 表达式括号匹配</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1981">P1981 表达式求值</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1175">P1175 表达式的转换</a></li>
</ul>
<h3 id="Part-7-3-队列"><a href="#Part-7-3-队列" class="headerlink" title="Part 7.3 队列"></a>Part 7.3 队列</h3><blockquote>
<p>队列，是一种先进先出（FIFO）的数据结构。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1540">P1540 机器翻译</a></li>
</ul>
<h3 id="Part-7-4-并查集"><a href="#Part-7-4-并查集" class="headerlink" title="Part 7.4 并查集"></a>Part 7.4 并查集</h3><blockquote>
<p>并查集常用于处理一些不相交集合的合并和查询问题。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1111">P1111 修复公路</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3958">P3958 奶酪</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1525">P1525 关押罪犯</a></li>
<li>[<del>P2024 [NOI2001]食物链</del>](<a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2024">https://www.luogu.org/problemnew/show/P2024</a>)</li>
<li>[<del>P1197 [JSOI2008]星球大战</del>](<a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1197">https://www.luogu.org/problemnew/show/P1197</a>)</li>
<li>[P1196 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1196">NOI2002]银河英雄传说</a></li>
<li>[P1955 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1955">NOI2015]程序自动分析</a></li>
</ul>
<h3 id="Part-7-5-堆"><a href="#Part-7-5-堆" class="headerlink" title="Part 7.5 堆"></a>Part 7.5 堆</h3><blockquote>
<p>堆总是一棵完全树，堆中某个节点的值总是不大于或不小于其父节点的值。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3378"><del>P3378 【模板】堆</del></a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1168">P1168 中位数</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2085">P2085 最小函数值</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2827">P2827 蚯蚓</a></li>
</ul>
<h3 id="Part-7-6-树状数组"><a href="#Part-7-6-树状数组" class="headerlink" title="Part 7.6 树状数组"></a>Part 7.6 树状数组</h3><blockquote>
<p>树状数组是一种简洁高效的树形数据结构。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3374"><del>P3374 【模板】树状数组 1</del></a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3368">P3368 【模板】树状数组 2</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1908">P1908 逆序对</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1966">P1966 火柴排队</a></li>
<li>[P1972 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1972">SDOI2009]HH的项链</a></li>
<li>[P3586 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3586">POI2015]LOG</a></li>
<li>[P4054 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4054">JSOI2009]计数问题</a></li>
<li>[P4113 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4113">HEOI2012]采花</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3960">P3960 列队</a></li>
</ul>
<h3 id="Part-7-7-线段树"><a href="#Part-7-7-线段树" class="headerlink" title="Part 7.7 线段树"></a>Part 7.7 线段树</h3><blockquote>
<p>线段树的通用性比树状数组更强，可以处理更多涉及区间操作的题目。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3372">P3372 【模板】线段树 1</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3373">P3373 【模板】线段树 2</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1382">P1382 楼房</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1471">P1471 方差</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1502">P1502 窗口的星星</a></li>
<li>[P2471 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2471">SCOI2007]降雨量</a></li>
<li>[P2824 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2824">HEOI2016/TJOI2016]排序</a></li>
<li>[P3722 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3722">AH2017/HNOI2017]影魔</a></li>
<li>[P4097 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4097">HEOI2013]Segment</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4198">P4198 楼房重建</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4513">P4513 小白逛公园</a></li>
<li>[P5324 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5324">BJOI2019]删数</a></li>
<li>[P5327 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5327">ZJOI2019]语言</a></li>
</ul>
<h3 id="Part-7-8-分块"><a href="#Part-7-8-分块" class="headerlink" title="Part 7.8 分块"></a>Part 7.8 分块</h3><blockquote>
<p>分块是一种非常通用的暴力方法，虽然效率不如线段树和树状数组，但可以解决很多线段树和树状数组处理不了的问题。</p>
</blockquote>
<ul>
<li>[P3870 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3870">TJOI2009]开关</a></li>
<li>[P1972 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1972">SDOI2009]HH的项链</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3396">P3396 哈希冲突</a></li>
<li>[P1494 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1494">国家集训队]小Z的袜子</a></li>
<li>[P1903 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1903">国家集训队]数颜色 / 维护队列</a></li>
<li>[P1975 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1975">国家集训队]排队</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3710">P3710 方方方的数据结构</a></li>
<li>[P4074 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4074">WC2013]糖果公园</a></li>
<li>[P4168 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4168">Violet]蒲公英</a></li>
<li>[P4119 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4119">Ynoi2018]未来日记</a></li>
<li>[P4117 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4117">Ynoi2018]五彩斑斓的世界</a></li>
</ul>
<h3 id="Part-7-9-点分治"><a href="#Part-7-9-点分治" class="headerlink" title="Part 7.9 点分治"></a>Part 7.9 点分治</h3><blockquote>
<p>点分治是一种可以高效统计树上路径信息的算法。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3806">P3806 【模板】点分治1</a></li>
<li>[P2634 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2634">国家集训队]聪聪可可</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2664">P2664 树上游戏</a></li>
<li>[P4292 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4292">WC2010]重建计划</a></li>
<li>[P4149 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4149">IOI2011]Race</a></li>
<li>[P3241 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3241">HNOI2015]开店</a></li>
</ul>
<h3 id="Part-7-10-主席树"><a href="#Part-7-10-主席树" class="headerlink" title="Part 7.10 主席树"></a>Part 7.10 主席树</h3><ul>
<li>[P2468 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2468">SDOI2010]粟粟的书架</a></li>
<li>[P3302 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3302">SDOI2013]森林</a></li>
<li>[P3168 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3168">CQOI2015]任务查询系统</a></li>
<li>[P4559 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4559">JSOI2018]列队</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2633">P2633 Count on a tree</a></li>
<li>[P3293 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3293">SCOI2016]美味</a></li>
<li>[P4618 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4618">SDOI2018]原题识别</a></li>
</ul>
<h3 id="Part-7-11-平衡树"><a href="#Part-7-11-平衡树" class="headerlink" title="Part 7.11 平衡树"></a>Part 7.11 平衡树</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3369">P3369 【模板】普通平衡树</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3391">P3391 【模板】文艺平衡树（Splay）</a></li>
<li>[P3850 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3850">TJOI2007]书架</a></li>
<li>[P4008 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4008">NOI2003]文本编辑器</a></li>
<li>[P5338 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5338">TJOI2019]甲苯先生的滚榜</a></li>
<li>[P2042 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2042">NOI2005]维护数列</a></li>
<li>[P1110 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1110">ZJOI2007]报表统计</a></li>
<li>[P3644 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3644">APIO2015]八邻旁之桥</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3765">P3765 总统选举</a></li>
<li>[P1486 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1486">NOI2004]郁闷的出纳员</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2710">P2710 数列</a></li>
<li>[P3224 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3224">HNOI2012]永无乡</a></li>
<li>[P3285 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3285">SCOI2014]方伯伯的OJ</a></li>
<li>[P5321 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5321">BJOI2019]送别</a></li>
</ul>
<h3 id="Part-7-12-树链剖分"><a href="#Part-7-12-树链剖分" class="headerlink" title="Part 7.12 树链剖分"></a>Part 7.12 树链剖分</h3><blockquote>
<p>树链剖分可以将任意一条树上路径划分成若干条连续的链，并用线段树等数据结构高效维护链上信息。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3384">P3384 【模板】树链剖分</a></li>
<li>[P3313 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3313">SDOI2014]旅行</a></li>
<li>[P2590 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2590">ZJOI2008]树的统计</a></li>
<li>[P2486 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2486">SDOI2011]染色</a></li>
<li>[P2146 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2146">NOI2015]软件包管理器</a></li>
<li>[P3178 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3178">HAOI2015]树上操作</a></li>
<li>[P3258 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3258">JLOI2014]松鼠的新家</a></li>
<li>[P4069 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4069">SDOI2016]游戏</a></li>
<li>[P4211 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4211">LNOI2014]LCA</a></li>
<li>[P5305 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5305">GXOI/GZOI2019]旧词</a></li>
</ul>
<h3 id="Part-7-13-树套树"><a href="#Part-7-13-树套树" class="headerlink" title="Part 7.13 树套树"></a>Part 7.13 树套树</h3><blockquote>
<p>树套树可以用来维护多维度信息。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3380">P3380 【模板】二逼平衡树（树套树）</a></li>
<li>[P1975 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1975">国家集训队]排队</a></li>
<li>[P3332 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3332">ZJOI2013]K大数查询</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4278">P4278 带插入区间K小值</a></li>
<li>[P1903 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1903">国家集训队]数颜色 / 维护队列</a></li>
<li>[P3759 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3759">TJOI2017]不勤劳的图书管理员</a></li>
<li>[P3242 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3242">HNOI2015]接水果</a></li>
<li>[P3248 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3248">HNOI2016]树</a></li>
</ul>
<h3 id="Part-7-14-动态树"><a href="#Part-7-14-动态树" class="headerlink" title="Part 7.14 动态树"></a>Part 7.14 动态树</h3><blockquote>
<p>Link-Cut Tree 可以用来解决动态树一类问题。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3690">P3690 【模板】Link Cut Tree （动态树）</a></li>
<li>[P3203 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3203">HNOI2010]弹飞绵羊</a></li>
<li>[P1501 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1501">国家集训队]Tree II</a></li>
<li>[P4338 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4338">ZJOI2018]历史</a></li>
<li>[P4312 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4312">COCI 2009] OTOCI / 极地旅行社</a></li>
<li>[P2387 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2387">NOI2014]魔法森林</a></li>
<li>[P3348 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3348">ZJOI2016]大森林</a></li>
<li>[P3703 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3703">SDOI2017]树点涂色</a></li>
<li>[P4172 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4172">WC2006]水管局长</a></li>
<li>[P4219 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4219">BJOI2014]大融合</a></li>
</ul>
<h3 id="Part-7-15-CDQ分治-amp-整体二分"><a href="#Part-7-15-CDQ分治-amp-整体二分" class="headerlink" title="Part 7.15 CDQ分治&amp;整体二分"></a>Part 7.15 CDQ分治&amp;整体二分</h3><blockquote>
<p>通过离线分治算法，我们可以避免使用一些高级数据结构。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3810">P3810 【模板】三维偏序（陌上花开）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1393">P1393 动态逆序对</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2617">P2617 Dynamic Rankings</a></li>
<li>[P3332 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3332">ZJOI2013]K大数查询</a></li>
<li>[P4169 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4169">Violet]天使玩偶/SJY摆棋子</a></li>
</ul>
<h3 id="Part-7-16-可持久化数据结构"><a href="#Part-7-16-可持久化数据结构" class="headerlink" title="Part 7.16 可持久化数据结构"></a>Part 7.16 可持久化数据结构</h3><blockquote>
<p>可持久化数据结构实现了在更新信息的时候保留历史版本。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3835">P3835 【模板】可持久化平衡树</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3919">P3919 【模板】可持久化数组（可持久化线段树/平衡树）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5055">P5055 【模板】可持久化文艺平衡树</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3834">P3834 【模板】可持久化线段树 1（主席树）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3402">P3402 【模板】可持久化并查集</a></li>
<li>[P5283 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5283">十二省联考2019]异或粽子</a></li>
</ul>
<h2 id="Part-8-图论"><a href="#Part-8-图论" class="headerlink" title="Part 8 图论"></a>Part 8 图论</h2><blockquote>
<p>图论是数学的一个分支，它以图为研究的对象。</p>
</blockquote>
<h3 id="Part-8-1-图的存储与遍历"><a href="#Part-8-1-图的存储与遍历" class="headerlink" title="Part 8.1 图的存储与遍历"></a>Part 8.1 图的存储与遍历</h3><blockquote>
<p>这里的图论内容都比较简单，涉及图的存储以及遍历图的方式。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2661">P2661 信息传递</a></li>
<li>[P2921 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2921">USACO08DEC]在农场万圣节Trick or Treat on the Farm</a></li>
</ul>
<h3 id="Part-8-2-最短路问题"><a href="#Part-8-2-最短路问题" class="headerlink" title="Part 8.2 最短路问题"></a>Part 8.2 最短路问题</h3><blockquote>
<p>很多题目都可以转化为最短路的模型。因此，掌握最短路算法非常重要。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3371">P3371 【模板】单源最短路径（弱化版）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4779">P4779 【模板】单源最短路径（标准版）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1144">P1144 最短路计数</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5001">P5001 魔法祝福</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1462">P1462 通往奥格瑞玛的道路</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1522">P1522 牛的旅行 Cow Tours</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1266">P1266 速度限制</a></li>
<li>[P3238 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3238">HNOI2014]道路堵塞</a></li>
<li>[P5304 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5304">GXOI/GZOI2019]旅行者</a></li>
</ul>
<h3 id="Part-8-3-树上问题"><a href="#Part-8-3-树上问题" class="headerlink" title="Part 8.3 树上问题"></a>Part 8.3 树上问题</h3><blockquote>
<p>作为一种特殊的图，树上的问题具有很多鲜明的特点。</p>
</blockquote>
<h4 id="Part-8-3-1-二叉树"><a href="#Part-8-3-1-二叉树" class="headerlink" title="Part 8.3.1 二叉树"></a>Part 8.3.1 二叉树</h4><blockquote>
<p>二叉树是一种特殊的树，它有很多特殊的性质。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1087">P1087 FBI树</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1030">P1030 求先序排列</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1305">P1305 新二叉树</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1229">P1229 遍历问题</a></li>
</ul>
<h4 id="Part-8-3-2-树的直径"><a href="#Part-8-3-2-树的直径" class="headerlink" title="Part 8.3.2 树的直径"></a>Part 8.3.2 树的直径</h4><blockquote>
<p>树的直径被定义为树上最远的两点间的距离。</p>
<p>计算树的直径，可以通过两遍 DFS 解决。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2195"><del>P2195 HXY造公园</del></a></li>
<li>[P3629 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3629">APIO2010]巡逻</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1099">P1099 树网的核</a></li>
</ul>
<h4 id="Part-8-3-3-最近公共祖先"><a href="#Part-8-3-3-最近公共祖先" class="headerlink" title="Part 8.3.3 最近公共祖先"></a>Part 8.3.3 最近公共祖先</h4><blockquote>
<p>两个点的最近公共祖先，即两个点的所有公共祖先中，离根节点最远的一个节点。</p>
<p>求解最近公共祖先，常用的方法是树上倍增或者树链剖分。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3379">P3379 【模板】最近公共祖先（LCA）</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3938">P3938 斐波那契</a></li>
<li>[P4281 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4281">AHOI2008]紧急集合 / 聚会</a></li>
</ul>
<h3 id="Part-8-4-生成树"><a href="#Part-8-4-生成树" class="headerlink" title="Part 8.4 生成树"></a>Part 8.4 生成树</h3><blockquote>
<p>用 $ n-1 $ 条边将图上的 $ n $ 个点连接起来，形成的树就被称为生成树。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3366">P3366 【模板】最小生成树</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1546">P1546 最短网络 Agri-Net</a></li>
<li>[P2330 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2330">SCOI2005]繁忙的都市</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1991">P1991 无线通讯网</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1967">P1967 货车运输</a></li>
</ul>
<h3 id="Part-8-5-拓扑排序"><a href="#Part-8-5-拓扑排序" class="headerlink" title="Part 8.5 拓扑排序"></a>Part 8.5 拓扑排序</h3><blockquote>
<p>将一个有向无环图排序，使得所有排在前面的节点不能依赖于排在后面的节点，这就是拓扑排序。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1113">P1113 杂务</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1983">P1983 车站分级</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1038">P1038 神经网络</a></li>
</ul>
<h3 id="Part-8-6-差分约束"><a href="#Part-8-6-差分约束" class="headerlink" title="Part 8.6 差分约束"></a>Part 8.6 差分约束</h3><blockquote>
<p>差分约束要解决的问题是：求出一组 $ n $ 元不等式的一组解，使得所有约束关系都能得到满足。</p>
</blockquote>
<ul>
<li>[P3275 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3275">SCOI2011]糖果</a></li>
<li>[P2294 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2294">HNOI2005]狡猾的商人</a></li>
<li>[P4926 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4926">1007]倍杀测量者</a></li>
</ul>
<h3 id="Part-8-7-图的连通性相关"><a href="#Part-8-7-图的连通性相关" class="headerlink" title="Part 8.7 图的连通性相关"></a>Part 8.7 图的连通性相关</h3><blockquote>
<p>利用 Tarjan 算法，我们可以解决很多与图的连通性相关的问题。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3387">P3387 【模板】缩点</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3388">P3388 【模板】割点（割顶）</a></li>
<li>[P2863 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2863">USACO06JAN]牛的舞会The Cow Prom</a></li>
<li>[P2746 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2746">USACO5.3]校园网Network of Schools</a></li>
<li>[P1407 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1407">国家集训队]稳定婚姻</a></li>
<li>[P2341 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2341">HAOI2006]受欢迎的牛</a></li>
<li>[P3225 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3225">HNOI2012]矿场搭建</a></li>
<li>[P5058 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5058">ZJOI2004]嗅探器</a></li>
<li>[P2515 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2515">HAOI2010]软件安装</a></li>
</ul>
<h3 id="Part-8-8-二分图"><a href="#Part-8-8-二分图" class="headerlink" title="Part 8.8 二分图"></a>Part 8.8 二分图</h3><blockquote>
<p>二分图上的不少问题都可以转化成网络流解决，当然也有独特的其他方法。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3386">P3386 【模板】二分图匹配</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2756">P2756 飞行员配对方案问题</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1559">P1559 运动员最佳匹配问题</a></li>
<li>[P2055 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2055">ZJOI2009]假期的宿舍</a></li>
<li>[P2825 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2825">HEOI2016/TJOI2016]游戏</a></li>
<li>[P3033 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3033">USACO11NOV]牛的障碍Cow Steeplechase</a></li>
<li>[P3731 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3731">HAOI2017]新型城市化</a></li>
</ul>
<h3 id="Part-8-9-网络流"><a href="#Part-8-9-网络流" class="headerlink" title="Part 8.9 网络流"></a>Part 8.9 网络流</h3><blockquote>
<p>网络流是图论中一个重要的分支，很多题目都可以通过建立网络流的模型来解决。</p>
</blockquote>
<h4 id="Part-8-9-1-最大流-最小割"><a href="#Part-8-9-1-最大流-最小割" class="headerlink" title="Part 8.9.1 最大流/最小割"></a>Part 8.9.1 最大流/最小割</h4><blockquote>
<p>最大流，即求网络中最大的流量。</p>
<p>最小割，即求一个边权最小的边集，使得源点和汇点不再连通。</p>
<p>可以证明，<strong>最大流=最小割</strong>，因此我们将最大流和最小割专题放在一起。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3376">P3376 【模板】网络最大流</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4722">P4722 【模板】最大流 加强版 / 预流推进</a></li>
<li>[P1345 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1345">USACO5.4]奶牛的电信Telecowmunication</a></li>
<li>[P2065 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2065">TJOI2011]卡片</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2774">P2774 方格取数问题</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2763">P2763 试题库问题</a></li>
<li>[P2472 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2472">SCOI2007]蜥蜴</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2765">P2765 魔术球问题</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2764">P2764 最小路径覆盖问题</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2766">P2766 最长不下降子序列问题</a></li>
<li>[P2805 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2805">NOI2009]植物大战僵尸</a></li>
<li>[P3749 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3749">六省联考2017]寿司餐厅</a></li>
<li>[P5039 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5039">SHOI2010]最小生成树</a></li>
</ul>
<h4 id="Part-8-9-2-费用流"><a href="#Part-8-9-2-费用流" class="headerlink" title="Part 8.9.2 费用流"></a>Part 8.9.2 费用流</h4><blockquote>
<p>在网络流中给边加上一个参数——费用，就出现了费用流。</p>
</blockquote>
<ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3381">P3381 【模板】最小费用最大流</a></li>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4016">P4016 负载平衡问题</a></li>
<li>[P4452 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4452">国家集训队]航班安排</a></li>
<li>[P2153 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2153">SDOI2009]晨跑</a></li>
<li>[P2053 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2053">SCOI2007]修车</a></li>
<li>[P3159 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3159">CQOI2012]交换棋子</a></li>
<li>[P2604 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2604">ZJOI2010]网络扩容</a></li>
<li>[P2050 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2050">NOI2012]美食节</a></li>
<li>[P3980 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3980">NOI2008]志愿者招募</a></li>
<li>[P4249 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4249">WC2007]剪刀石头布</a></li>
<li>[P5331 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5331">SNOI2019]通信</a></li>
</ul>
<h3 id="Part-8-10-2-SAT"><a href="#Part-8-10-2-SAT" class="headerlink" title="Part 8.10 2-SAT"></a>Part 8.10 2-SAT</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4782">P4782 【模板】2-SAT 问题</a></li>
<li>[P3825 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3825">NOI2017]游戏</a></li>
<li>[P5332 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5332">JSOI2019]精准预测</a></li>
</ul>
<h3 id="Part-8-11-虚树"><a href="#Part-8-11-虚树" class="headerlink" title="Part 8.11 虚树"></a>Part 8.11 虚树</h3><ul>
<li>[P2495 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2495">SDOI2011]消耗战</a></li>
<li>[P3233 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3233">HNOI2014]世界树</a></li>
<li>[P5360 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5360">SDOI2019]世界地图</a></li>
</ul>
<h3 id="Part-8-12-矩阵树定理"><a href="#Part-8-12-矩阵树定理" class="headerlink" title="Part 8.12 矩阵树定理"></a>Part 8.12 矩阵树定理</h3><blockquote>
<p>矩阵树定理可以解决图的生成树计数问题。</p>
</blockquote>
<ul>
<li>[P4111 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4111">HEOI2015]小Z的房间</a></li>
<li>[P2144 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2144">FJOI2007]轮状病毒</a></li>
<li>[P3317 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3317">SDOI2014]重建</a></li>
<li>[P4208 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4208">JSOI2008]最小生成树计数</a></li>
</ul>
<h2 id="Part-9-计算几何"><a href="#Part-9-计算几何" class="headerlink" title="Part 9 计算几何"></a>Part 9 计算几何</h2><blockquote>
<p>试着用计算机来解决几何问题吧！</p>
</blockquote>
<h3 id="Part-9-1-凸包"><a href="#Part-9-1-凸包" class="headerlink" title="Part 9.1 凸包"></a>Part 9.1 凸包</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2742">P2742 【模板】二维凸包</a></li>
<li>[P2287 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2287">HNOI2004]最佳包裹</a></li>
<li>[P3829 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3829">SHOI2012]信用卡凸包</a></li>
<li>[P4680 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4680">Ynoi2018]末日时在做什么?有没有空?可以来拯救吗?</a></li>
<li>[P4557 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4557">JSOI2018]战争</a></li>
<li>[P5403 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5403">CTS2019]田野</a></li>
</ul>
<h3 id="Part-9-2-旋转卡壳"><a href="#Part-9-2-旋转卡壳" class="headerlink" title="Part 9.2 旋转卡壳"></a>Part 9.2 旋转卡壳</h3><ul>
<li><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1452">P1452 Beauty Contest</a></li>
<li>[P3187 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3187">HNOI2007]最小矩形覆盖</a></li>
</ul>
<h3 id="Part-9-3-半平面交"><a href="#Part-9-3-半平面交" class="headerlink" title="Part 9.3 半平面交"></a>Part 9.3 半平面交</h3><ul>
<li>[P3256 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3256">JLOI2013]赛车</a></li>
<li>[P2600 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2600">ZJOI2008]瞭望塔</a></li>
<li>[P4196 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4196">CQOI2006]凸多边形</a></li>
<li>[P3297 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3297">SDOI2013]逃考</a></li>
<li>[P4250 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4250">SCOI2015]小凸想跑步</a></li>
<li>[P5328 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5328">ZJOI2019]浙江省选</a></li>
</ul>
<h2 id="Part-10-杂项"><a href="#Part-10-杂项" class="headerlink" title="Part 10 杂项"></a>Part 10 杂项</h2><h3 id="Part-10-1-模拟退火"><a href="#Part-10-1-模拟退火" class="headerlink" title="Part 10.1 模拟退火"></a>Part 10.1 模拟退火</h3><blockquote>
<p>模拟退火是一种随机化算法。当一个问题的方案数量极大（甚至是无穷的）而且不是一个单峰函数时，我们常使用模拟退火求解。</p>
</blockquote>
<ul>
<li>[P1337 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1337">JSOI2004]平衡点 / 吊打XXX</a></li>
<li>[P2503 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P2503">HAOI2006]均分数据</a></li>
<li>[P3878 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3878">TJOI2010]分金币</a></li>
</ul>
<h3 id="Part-10-2-0-1-分数规划"><a href="#Part-10-2-0-1-分数规划" class="headerlink" title="Part 10.2 0/1 分数规划"></a>Part 10.2 0/1 分数规划</h3><ul>
<li>[P4377 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4377">USACO18OPEN]Talent Show</a></li>
<li>[P3199 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3199">HNOI2009]最小圈</a></li>
<li>[P3288 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3288">SCOI2014]方伯伯运椰子</a></li>
<li>[P3705 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3705">SDOI2017]新生舞会</a></li>
<li>[P4322 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4322">JSOI2016]最佳团体</a></li>
</ul>
<h3 id="Part-10-3-奇怪的题目"><a href="#Part-10-3-奇怪的题目" class="headerlink" title="Part 10.3 奇怪的题目"></a>Part 10.3 奇怪的题目</h3><blockquote>
<p>OI 界中有一些非常规套路的题目，这里放出来分享。</p>
</blockquote>
<ul>
<li>[P4920 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4920">WC2015]未来程序</a></li>
<li>[P5042 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5042">国家集训队] 丢失的题面（ydc的题面）</a></li>
<li>[P5285 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5285">十二省联考2019]骗分过样例</a></li>
<li>[P5246 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5246">集训队互测2016] 消失的源代码</a></li>
</ul>
<h3 id="Part-10-4-非传统题"><a href="#Part-10-4-非传统题" class="headerlink" title="Part 10.4 非传统题"></a>Part 10.4 非传统题</h3><blockquote>
<p>在 NOI 等比赛中，非传统题正越来越频繁出现。</p>
<p>非传统题主要包括以下几类：提交答案题，交互题，通信题。</p>
<p>因为洛谷目前只支持提交答案题，因此这里暂时只列出提交答案题。</p>
</blockquote>
<h4 id="Part-10-4-1-提交答案题"><a href="#Part-10-4-1-提交答案题" class="headerlink" title="Part 10.4.1 提交答案题"></a>Part 10.4.1 提交答案题</h4><blockquote>
<p>给你一些输入，你只需要提交这些输入对应的答案，即为提交答案题。</p>
</blockquote>
<ul>
<li><p>[P1335 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1335">NOI2013]小Q的修炼</a></p>
</li>
<li><p>[P1737 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P1737">NOI2016]旷野大计算</a></p>
</li>
<li><p><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3614">P3614 yyy棋 II</a></p>
</li>
<li><p>[P3640 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3640">APIO2013]出题人</a></p>
</li>
<li><p>[P3782 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3782">WC2017]排序</a></p>
</li>
<li><p><a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P3836">P3836 Nowruz 诺鲁孜节</a></p>
</li>
<li><p>[P4920 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P4920">WC2015]未来程序</a></p>
</li>
<li><p>[P5402 <a target="_blank" rel="noopener" href="https://www.luogu.org/problemnew/show/P5402">CTS2019]无处安放</a></p>
</li>
</ul>

    </div>

    
    
    

    <footer class="post-footer">

        

          <div class="post-nav">
            <div class="post-nav-item">
                <a href="/2019/【luogu-2573】【SCOI2012】滑雪/" rel="prev" title="【luogu-2573】【SCOI2012】滑雪">
                  <i class="fa fa-chevron-left"></i> 【luogu-2573】【SCOI2012】滑雪
                </a>
            </div>
            <div class="post-nav-item">
                <a href="/2019/【luogu-3304】【SDOI2013】直径/" rel="next" title="【luogu-3304】【SDOI2013】直径">
                  【luogu-3304】【SDOI2013】直径 <i class="fa fa-chevron-right"></i>
                </a>
            </div>
          </div>
    </footer>
  </article>
  
  
  



      
    <div class="comments" id="valine-comments"></div>

<script>
  window.addEventListener('tabs:register', () => {
    let { activeClass } = CONFIG.comments;
    if (CONFIG.comments.storage) {
      activeClass = localStorage.getItem('comments_active') || activeClass;
    }
    if (activeClass) {
      const activeTab = document.querySelector(`a[href="#comment-${activeClass}"]`);
      if (activeTab) {
        activeTab.click();
      }
    }
  });
  if (CONFIG.comments.storage) {
    window.addEventListener('tabs:click', event => {
      if (!event.target.matches('.tabs-comment .tab-content .tab-pane')) return;
      const commentClass = event.target.classList[1];
      localStorage.setItem('comments_active', commentClass);
    });
  }
</script>

    </div>
  </main>

  <footer class="footer">
    <div class="footer-inner">
      

      

<div class="copyright">
  
  &copy; 2018 – 
  <span itemprop="copyrightYear">2021</span>
  <span class="with-love">
    <i class="fa fa-heart"></i>
  </span>
  <span class="author" itemprop="copyrightHolder">舒雨墨</span>
</div>
<div class="wordcount">
  <span class="post-meta-item">
    <span class="post-meta-item-icon">
      <i class="fa fa-chart-line"></i>
    </span>
    <span title="站点总字数">319k</span>
  </span>
  <span class="post-meta-item">
    <span class="post-meta-item-icon">
      <i class="fa fa-coffee"></i>
    </span>
    <span title="站点阅读时长">4:50</span>
  </span>
</div>
  <div class="powered-by">由 <a href="https://hexo.io/" class="theme-link" rel="noopener" target="_blank">Hexo</a> & <a href="https://theme-next.js.org/mist/" class="theme-link" rel="noopener" target="_blank">NexT.Mist</a> 强力驱动
  </div>

    </div>
  </footer>

  
  <script src="//cdn.jsdelivr.net/npm/animejs@3.2.0/lib/anime.min.js"></script>
  <script src="//cdn.jsdelivr.net/npm/@next-theme/pjax@0.4.0/pjax.min.js"></script>
<script src="/js/utils.js"></script><script src="/js/motion.js"></script><script src="/js/schemes/muse.js"></script><script src="/js/next-boot.js"></script>
  <script>
var pjax = new Pjax({
  selectors: [
    'head title',
    '.page-configurations',
    '.main-inner',
    '.post-toc-wrap',
    '.languages',
    '.pjax'
  ],
  analytics: false,
  cacheBust: false,
  scrollRestoration: false,
  scrollTo: !CONFIG.bookmark.enable
});

document.addEventListener('pjax:success', () => {
  pjax.executeScripts(document.querySelectorAll('script[data-pjax], .pjax script'));
  NexT.boot.refresh();
  // Define Motion Sequence & Bootstrap Motion.
  if (CONFIG.motion.enable) {
    NexT.motion.integrator
      .init()
      .add(NexT.motion.middleWares.subMenu)
      .add(NexT.motion.middleWares.postList)
      .bootstrap();
  }
  const hasTOC = document.querySelector('.post-toc');
  document.querySelector('.sidebar-inner').classList.toggle('sidebar-nav-active', hasTOC);
  document.querySelector(hasTOC ? '.sidebar-nav-toc' : '.sidebar-nav-overview').click();
  NexT.utils.updateSidebarPosition();
});
</script>


  
  <script data-pjax>
    (function(){
      var bp = document.createElement('script');
      var curProtocol = window.location.protocol.split(':')[0];
      bp.src = (curProtocol === 'https') ? 'https://zz.bdstatic.com/linksubmit/push.js' : 'http://push.zhanzhang.baidu.com/push.js';
      var s = document.getElementsByTagName("script")[0];
      s.parentNode.insertBefore(bp, s);
    })();
  </script>




  <script src="/js/local-search.js"></script>












  






<script data-pjax>
  (function() {
    function leancloudSelector(url) {
      return document.getElementById(url).querySelector('.leancloud-visitors-count');
    }

    function addCount(Counter) {
      const visitors = document.querySelector('.leancloud_visitors');
      const url = decodeURI(visitors.id);
      const title = visitors.dataset.flagTitle;

      Counter('get', '/classes/Counter?where=' + encodeURIComponent(JSON.stringify({ url })))
        .then(response => response.json())
        .then(({ results }) => {
          if (results.length > 0) {
            const counter = results[0];
            leancloudSelector(url).innerText = counter.time + 1;
            Counter('put', '/classes/Counter/' + counter.objectId, { time: { '__op': 'Increment', 'amount': 1 } })
              .catch(error => {
                console.error('Failed to save visitor count', error);
              });
          } else {
              Counter('post', '/classes/Counter', { title, url, time: 1 })
                .then(response => response.json())
                .then(() => {
                  leancloudSelector(url).innerText = 1;
                })
                .catch(error => {
                  console.error('Failed to create', error);
                });
          }
        })
        .catch(error => {
          console.error('LeanCloud Counter Error', error);
        });
    }

    function showTime(Counter) {
      const visitors = document.querySelectorAll('.leancloud_visitors');
      const entries = [...visitors].map(element => {
        return decodeURI(element.id);
      });
      Counter('get', '/classes/Counter?where=' + encodeURIComponent(JSON.stringify({ url: { '$in': entries } })))
        .then(response => response.json())
        .then(({ results }) => {
          for (let url of entries) {
            const target = results.find(item => item.url === url);
            leancloudSelector(url).innerText = target ? target.time : 0;
          }
        })
        .catch(error => {
          console.error('LeanCloud Counter Error', error);
        });
    }

    const { app_id, app_key, server_url } = {"enable":true,"app_id":"Tw3wqSuCQwL4zK5pGCd6BkKa-gzGzoHsz","app_key":"lwlhdaYvNPPDLhBEGeUegbH6","server_url":null,"security":false};
    function fetchData(api_server) {
      const Counter = (method, url, data) => {
        return fetch(`${api_server}/1.1${url}`, {
          method,
          headers: {
            'X-LC-Id'     : app_id,
            'X-LC-Key'    : app_key,
            'Content-Type': 'application/json',
          },
          body: JSON.stringify(data)
        });
      };
      if (CONFIG.page.isPost) {
        if (location.hostname == '127.0.0.1' || location.hostname == 'localhost') ;
        else addCount(Counter);
      }
      if (document.querySelectorAll('.post-title-link').length >= 1 || document.querySelectorAll('.post-title').length >= 1) {
        showTime(Counter);
      }
    }

    const api_server = app_id.slice(-9) !== '-MdYXbMMI' ? server_url : `https://${app_id.slice(0, 8).toLowerCase()}.api.lncldglobal.com`;

    if (api_server) {
      fetchData(api_server);
    } else {
      fetch('https://app-router.leancloud.cn/2/route?appId=' + app_id)
        .then(response => response.json())
        .then(({ api_server }) => {
          fetchData('https://' + api_server);
        });
    }
  })();
</script>


    <div class="pjax">
  

  
      <script>
  if (typeof MathJax === 'undefined') {
    window.MathJax = {
      tex: {
        inlineMath: {'[+]': [['$', '$']]},
        tags: 'ams'
      },
      options: {
        renderActions: {
          findScript: [10, doc => {
            document.querySelectorAll('script[type^="math/tex"]').forEach(node => {
              const display = !!node.type.match(/; *mode=display/);
              const math = new doc.options.MathItem(node.textContent, doc.inputJax[0], display);
              const text = document.createTextNode('');
              node.parentNode.replaceChild(text, node);
              math.start = {node: text, delim: '', n: 0};
              math.end = {node: text, delim: '', n: 0};
              doc.math.push(math);
            });
          }, '', false],
          insertedScript: [200, () => {
            document.querySelectorAll('mjx-container').forEach(node => {
              const target = node.parentNode;
              if (target.nodeName.toLowerCase() === 'li') {
                target.parentNode.classList.add('has-jax');
              }
            });
          }, '', false]
        }
      }
    };
    const script = document.createElement('script');
    script.src = '//cdn.jsdelivr.net/npm/mathjax@3.1.0/es5/tex-mml-chtml.js';
    script.defer = true;
    document.head.appendChild(script);
  } else {
    MathJax.startup.document.state(0);
    MathJax.typesetClear();
    MathJax.texReset();
    MathJax.typeset();
  }
</script>

    

  
<script>
NexT.utils.loadComments('#valine-comments', () => {
  NexT.utils.getScript('//cdn.jsdelivr.net/npm/valine@1.4.14/dist/Valine.min.js', () => {
    new Valine(Object.assign({
      el  : '#valine-comments',
      path: "2019/做题计划/",
    }, {"enable":true,"appId":"Tw3wqSuCQwL4zK5pGCd6BkKa-gzGzoHsz","appKey":"lwlhdaYvNPPDLhBEGeUegbH6","placeholder":"Just go go","avatar":"mm","meta":["nick","mail","link"],"pageSize":10,"lang":"zh-cn","visitor":false,"comment_count":true,"recordIP":true,"serverURLs":null,"enableQQ":true,"requiredFields":[]}
    ));
  }, window.Valine);
});
</script>

    </div>
</body>
</html>
